Exponential stability of nonlinear systems We consider a class of nonlinear impulsive systems with delayed impulses, where the time delays in impulses exist between two consecutive impulse instants. Furthermore, the criteria on noise-to-state stability in the moment of a special class of NRFSs, named neutral random delay nonlinear systems, are derived. This paper presents theoretical results on the robustness of the exponential stability of nonlinear systems in the presence of time delays and random disturbances. Employing the Lyapunov function method and the subsequence technique, the sufficient conditions for exponential stability of the p t h moments (ES- p t h) of the system are established. Such a theorem has been widely used for stability analysis and control design of nonlinear systems in the past several decades (Ito and Jiang, 2009, Jiang et al. A. If an ISS Lyapunov function is the exponential one, we provide a stronger result, which guarantees uniform ISS of the whole system over sequences satisfying the generalized average dwell-time condition. A weakened concept of Fréchet differentiability ((Y,X)-Fréchet differentiability) for nonlinear operators defined on Banach spaces is proposed, including the introduction of an alternative space (Y) in the analysis. edu. Almost surely exponential stability of mode-dependent stochastic coupled nonlinear systems with semi-Markovian jump. The Hausdorff dynamical systems proposed in this paper have potential applications in modeling complex multi-scale physical processes which exhibit stretched exponential decay phenomena [23], [24], [25]. Download Citation | On Jul 1, 2024, Weilian Liu and others published Exponential stability of nonlinear delay systems with delayed impulses: A novel comparison approach | Find, read and cite all In [28], a system argumentation approach was introduced to establish stability criterion for delay-free autonomous systems with delayed impulses. eorem 4. The single time-delay and multiple time-delays cases are respectively considered. Author links open overlay panel Yu Kang a b c, Niankun Zhang a, Guoyong Chen a. Furthermore, several characterizations for the exponential stability of a class of nonlinear This paper deals with the practical exponential stability of two-dimensional (2-D) nonlinear switched positive systems with impulse, disturbance and all modes unstable. Exponential stability is a form of asymptotic stability, valid for more general dynamical systems. By using the switched Lyapunov function method, sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained. In this paper, we are concerned with the stability of stochastic nonlinear delay systems. This method has been applied to systems with time delays [20], [21], [22] and is also adopted in the present paper. Generally speaking, the linearization method requires that the vector field of the original nonlinear system is continuously differentiable. convergence control scheme based on the time varying exponential function is demonstrated for a class of discrete-time nonlinear systems. To conquer the difficulties induced by time-varying parameters, we firstly put forward comparison theorem associated with a method that doesn’t involve any Lyapunov function and is commonly utilized in positive systems to set up new stability criteria exponential stability of the zero solution were established and estimates of exponen-tial decay of solutions at in nity have been obtained. Note that the systems considered in these papers have extensive applications in Hopfield neural exponential stability of nonlinear discrete-time systems Morgan Louedec, Luc Jaulin , Christophe Viel´ Abstract—This paper presents a guaranteed numerical method for proving the exponential stability of an n-dimensional nonlin-ear discrete-time system. This article is devoted to stability analysis of stochastic nonlinear delay systems subject to multiple periodic impulses. The main purpose of this paper is to propose an unified approach for studying exponential stability of a general class of time-varying switched systems, described by nonlinear functional differential equations, that is based on the comparison principle and the average dwell time (ADT) switching concept [5], [35], [36] (that will be highlighted in more details in the next The second Lyapunov method was extended to abstract nonlinear time-delay systems in the Banach spaces in Wang (1994a), and was applied to stability analysis of some scalar heat/wave equations with constant delays and with the Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study. By extending the traditional comparison principle, delay effects on continuous and discrete dynamics of the system are estimated, based on which, the internal relationship between delays, parameters of impulsive control, and continuous Dong J G. It is well known that time delays and additive noises may derail the stability of nonlinear systems. Moreover, the influence of neutral item can be considered in nonlinear systems via intermittent random noise. Show more. In this paper, exponential stability of nonlinear systems with impulse time window, disturbance input and bounded gain error is investigated. Different from the Considering technology limitation or device restriction in practical application, we formulate new nonlinear systems with bounded gain error, which contain switched control and This paper studies the robust stability of global exponential stability of nonlinear stochastic systems in the presence of time-varying delays and neutral terms. jfranklin. During the last decades, global exponential stability In this section, we will quantitatively analyse the effect of time delay and neutral term on global exponential stability of non-linear systems. An example is provided In Section 4. According to impulsive control theory, we present some Lyapunov-based This paper presents linkage-constraint criteria to guarantee the robustness of global exponential stability (RoGES) for a class of generalized nonlinear bidirectional associative memory (BAM) systems in the presence of derivative contraction coefficients and piecewise constant arguments (NBAM-dp system). By a novel approach, some explicit criteria for the exponential stability in mean square of such systems are derived. 4024-4034. Moreover, exponential stabilities of nonlinear systems have been investigated during the past few years and the references therein. The considered problem is a more general version compared with linear In this paper, we have studied the exponential stability results of fractional order nonlinear sampled-data control systems as a basic tool. The basic idea here is to transform the original system with slowly time-varying delays into an equivalent switched system with specific switching signals. However, tions for the exponential stability of the zero solution to the nonlinear system (1. Crossref. Such function can successfully eliminate the impulsive and switching jump phenomenon. Using the average Moreover, we also introduce a number of assumptions, definitions and a lemma. Super-exponential tracking for nonlinear systems with the utilization of a time-varying feedback in which the convergence rate can be pre-assigned is given in [29] . First, the mathematical model for a new kind of hybrid systems is proposed. Int J Robust Nonlinear Control, 2016, 26: 3118–3129. The existence and uniqueness, pth moment practically exponential stability and quasi surely globally practically uniformly exponential stability of the system are studied In Section 3. The cyclic-small-gain theorem is significantly extended in such a way that the interconnected system is proved to be globally exponentially stable, an exponential converging upper bound of state norm is obtained Sufficient conditions guaranteeing Lyapunov stability, asymptotic stability and exponential stability of nonlinear two-dimensional continuous–discrete systems are proposed. Practically, however, one is concerned not only with the stability of a system but also with the decay rate (also called the convergence rate), because the transient process of a system can The main contributions of the paper can be summarized as: (i) absolute exponential stability is stronger than absolute asymptotical stability in the literature, (ii) multiple Lyapunov–Krasovskii functionals are less conservative than common Lyapunov–Krasovskii functional, and (iii) the obtained results can be applied not only for switched nonlinear positive In this paper, we deal with a class of neutral random nonlinear systems. The Takagi and Sugeno (T-S) fuzzy model is employed to approximate the subnonlinear dynamic systems. Robust performance of nonlinear systems has attracted phenomenal worldwide attention. , 1996). 12. Both cases of time-delays namely constant and time-varying delays are treated in the switched singular systems. 1. A novel type of piecewise Lyapunov functionals is constructed to derive the exponential This paper concerns exponential stability of positive nonlinear dynamical systems on time scales. Hammami,3 and I. A. A continuously differentiable Lyapunov function with indefinite derivative is introduced, which generalises classic Lyapunov function method. Where we consider a type of nonnegative impulses, which do not need to be in step with the switching behaviors in the One of the main results in a recent paper [P. This article investigates the global exponential stability of the nonlinear delayed systems with logically selected impulses. It is worth noting that the definition of globally We study asymptotic stability of a class of non-autonomous stochastic delay lattice systems driven by a multiplicative white noise. Abbes4 UDC 517. 9 We solve the following twofold problem: In the ﬁrst part, we deduce Lyapunov sufﬁcient conditions for the practical uniform exponential stability of nonlinear perturbed systems under different condi- This paper studies the exponential stability of nonlinear delay systems by means of event-triggered impulsive control (ETIC) approach, where impulsive instants are determined by a Lyapunov-based Local exponential (exp. The robust exponential stability conditions are presented by Lyapunov–Razumikhin method. With the rise of research interest in large-scale and network This article investigates the exponential stability of nonlinear discrete-time systems with time-varying state delay and delayed impulses, where the delays in impulses are not fixed. Stability of Nonlinear Systems By Guanrong Chen Department of Electronic Engineering City University of Hong Kong Kowloon, Hong Kong SAR, China gchen@ee. [1] A. Keywords: Time scale; Switched systems; Stability analysis; Exponential stability. In recent years, the studies on the stability problem for SMJSs have gained considerable attention. , time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with As an important class of hybrid systems, switched systems arise in many practical processes that cannot be described by exclusively continuous or exclusively discrete models, such as manufacturing, communication networks, automotive engineering control and chemical processes (see, e. We first introduce a novel piecewise Lyapunov–Razumikhin function. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. In this paper, we investigate the p th moment exponential stability of impulsive random delayed nonlinear systems (RDNS) with average-delay impulses. Recently, the dynamical analysis of CFO differential systems has been performed [10], [11]. Practical consequences An Furthermore, three examples are given to illustrate the correctness of our results. Stability problem of switched nonlinear time-varying systems (SNTVS) with mixed delays is presented in this paper. Special attention is paid to neutrally stable systems such as some two-dimensional system descriptions of vehicle platoons, which may be stable or asymptotically stable but never In this article, we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to uncertainties. Recently, a special class of switched nonlinear systems, whose system matrices are Metzler and nonlinear functions satisfy the sector conditions, was studied in [14], [15], [16], [17]. 1. An example is First of all it is a local exponential stability. Input-to-state exponential stability (ISES) is a robust stability property for nonlinear systems subject to external inputs. Control Theory Appl. <abstract> This paper is concerned with the stability of nonlinear time-varying perturbed system on time scales under the assumption that the corresponding linear time-varying nominal system is uniformly exponentially stable. It is well known that deviating argument and stochastic disturbance may derail the evolution properties of nonlinear systems. and Zhang Y. By employing Lypaunov–Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and e λt This paper focuses on discussing the stability of time-varying switched impulsive nonlinear systems (TVSINSs). Some examples illustrate these results. establish some veriﬁable criteria for exponential stability of the zero solution of switched nonlinear FDE system under arbitrary switching, satisfying some ADT assumptions. When the non-autonomous deterministic Delays-dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result, and significant improvement of the estimate of stability limit over some existing results in the literature is given. Since the stability of switched systems with non-random switching signals is usually considered by using the dwell/average dwell times approach, the existing methods for highly non-linear stochastic systems with Markovian switching signals Semantic Scholar extracted view of "Exponential stability of neutral hybrid nonlinear systems via aperiodically intermittent stochastic noise: Average skills" by Chenxi Zhang et al. Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i. Then the following issue has become a major bottleneck: for a given globally exponentially stable nonlinear system, the perturbed nonlinear It provides an effective method to deal with the system stability under the uncertain input. Through considering performance-index-based adaptive switching control under a general framework, sufficient conditions are proposed and proved to ensure global generalized exponential stability and global finite-time Index Terms—Nonlinear stochastic delayed systems; pth mo-ment exponential stability; almost surely exponential stability; G-Brownian motion; existence and uniqueness I. We first extend the well-known Datko lemma to the framework of the considered class of systems. By introducing a model transformation and using a novel method which does not involve the Lyapunov–Krasovskii functional, new explicit criteria for exponential stability of the system under arbitrary switching have been established in terms of Systems that are not LTI are exponentially stable if their convergence is bounded by exponential decay. In general, exponential stability of a system can not be characterized by the spectrum of its matrix. sysconle. hk In Encyclopedia of RF and Microwave Engineering, Wiley, The absolute stability investigated in the above-mentioned works is defined as global asymptotic stability tolerating any nonlinear perturbations with special constraints. e. Besides standard cases of continuous time R and discrete time h Z = {h k: k ∈ Z} (where Z denotes the set of integers) there are many interesting and useful time scales. This paper focuses on the stability analysis and control of adaptive switching systems by establishing Lyapunov-based logic switching rules. The International Journal of Robust and Nonlinear Control promotes development of analysis and design techniques for uncertain linear and nonlinear systems. The problem of delay-dependent stability in the mean square sense for stochastic systems In this paper, we study exponential stability of switched time-varying systems with bounded delays and nonlinear disturbances. A new troublesome problem is that the neutral terms In this paper, we consider a class of nonlinear stochastic systems with respect to neutral terms and time-varying delays. To state our results, we introduce some notation. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied Mathematics Letters 25 (2012) 1208–1213] is extended to a more general nonlinear differential system with time-varying delays. Deﬁnition 1. The asymptotic stability criteria relying on delays sizes for nonlinear hybrid neutral stochastic systems with constant delays had already been explored. Exponential stability of homogeneous positive systems of degree one with time-varying delays. Yanqi Zhang, Yanqi Zhang. 009) PRACTICAL SEMIGLOBAL UNIFORM EXPONENTIAL STABILITY OF NONLINEAR NONAUTONOMOUS SYSTEMS A. This paper addresses the exponential stability issue of discrete-time switched nonlinear systems by means of the linearization approach. IEEE Trans Autom Control, 64 (10) (2019), pp. g. Under the mode-dependent interval dwell time switching, new criteria such that 2-D nonlinear switched positive systems achieve practical exponential stability are derived. The reader is referred to the literature [18], [19], [20] for more detailed information. It is shown that the time delay in impulses This paper addresses decentralized exponential stability problem for a class of nonlinear large-scale systems with time-varying delay in interconnection is considered. The existence and uniqueness of the solution to neutral random functional nonlinear systems (NRFSs) are established. However, compared to the abundant theoretical results on global exponential stability (GES) in integer-order differential equations with time delay and impulses, there is a scarcity of research on the exponential stability of conformable fractional-order nonlinear differential systems (CFNDSs) considering both impulse effects and time-varying The exponential stability problem for impulsive systems subject to double statedependent delays is studied in this paper, where state-dependent delay (SDD) is involved in both continuous dynamics In addition, we study nonlinear non-instantaneous impulsive equations and investigate existence, uniqueness of their solutions and Ulam-Hyers-Rassias stability under the restriction of exponential growth or stable conditions for noninstantaneous impulsive Cauchy matrix, respectively, which provide an approach to find approximate solution to nonlinear non-instantaneous impulsive Zong G. This manuscript analyzed the delay-dependent stability problem for non-linear switched singular time-delay systems based on average dwell time and delay decomposition approach. ) stability of nonlinear distributed parameter, i. 002 Corpus ID: 15977552; Exponential stability of hybrid switched nonlinear singular systems with time-varying delay @article{Zamani2013ExponentialSO, title={Exponential stability of hybrid switched nonlinear singular systems with time-varying delay}, author={Iman Zamani and Masoud Shafiee and Asier Ibeas}, journal={J. In this paper we address the exponential stability of nonlinear time-delay systems with more general delayed impulses which include (2) as a special case. Furthermore, the theoretical results for homogeneous positive nonlinear systems are generalized by obtaining the stability condition for switched homogeneous positive nonlinear systems with degree less than or equal to one. 021 Corpus ID: 19848091; Absolute exponential stability and stabilization of switched nonlinear systems @article{Zhang2014AbsoluteES, title={Absolute exponential stability and stabilization of switched nonlinear systems}, author={Junfeng Zhang and Zhengzhi Han and Fubo Zhu and Xudong Zhao}, journal={Syst. 111609 Corpus ID: 268311358; Exponential stability analysis of switched nonlinear systems: A linearization method @article{Liu2024ExponentialSA, title={Exponential stability analysis of switched nonlinear systems: A linearization method}, author={Xingwen Liu and Zumei Chen and Kaibo Shi and Min Li and Shouming Zhong}, Request PDF | Exponential practical stability of nonlinear impulsive systems: Converse theorem and applications | This paper investigates the practical exponential stability of equilibrium for In this paper we address the exponential stability of nonlinear time-delay systems with more general delayed impulses which include (2) as a special case. Integral input-to-state stability of nonlinear control systems with delays Chaos Solitons Fractals 34 420-427 2007. This method also finds positive invariant ellipsoids. An alternative approach to the standard Lyapunov–Krasovskii function is used to guarantee the positivity of the system. Int J Robust Nonlin Control, 2018, 28: 5590–5604. The global exponential stability for a type of continuous-time impulsive switched positive nonlinear systems (ISPNSs) with average dwell time (ADT) switching and mode-dependent impulsive effects is explored in this research. They ensure that the nonlinear With a view to the unfavorable impact of the inevitable exogenous interferences for the practical engineering and signal transmission, here we focus on the robustness of global exponential stability for nonlinear dynamical systems subject to piecewise constant arguments, neutral terms and stochastic disturbances (SNPNDS). Author links open overlay panel within stochastic switching systems to enhance the classical Lyapunov stability theorem and further deepen the stability analysis of nonlinear systems extensively, as evidenced by Remark 1. Wu X, Zhang Y. 2024. We then investigate the exponential stability of the considered systems. Lyapunov-based sufficient conditions for exponential stability with respect to destabilizing delayed impulses and stabilizing delayed impulses are established, respectively. Google Scholar. The ISS for reaction–diffusion systems (RDSs) without Markovian switching has been considered in [12]. The problem of global exponential stability (GES) for nonlinear delay impulsive systems is investigated in this paper. The positive and exponential stability for a class of switched non-linear systems under minimum dwell time switching is studied, whose non-linear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. In particular, there are important implications in the study of exponential stability for stochastic dynamic systems [19], [20] which is meaningful to estimate the convergence rate of stochastic systems in practice. . Exponential stability of nonlinear systems with impulsive effects and disturbance input Download PDF. S. Frankl. We consider a class of nonlinear impulsive systems with delayed impulses, where the time delays in impulses DOI: 10. ). Exponential stability of impulsive switched systems with delays 213 This paper shall focus on robust exponential stability for system (1) and the deﬁnition is as follows. Indeed, for a nonlinear hyperbolic system even the global well-posedness is usually impossible to guarantee for regular norms such as the C 1 and H 2 that will be studied in the following. Stability of switched positive nonlinear systems. Future works will focus on the stability of random perturbation nonlinear systems via intermittent random noise when delay is random variable. If the matrix H(t) satis es the DOI: 10. (1). In the framework of partial unknown states, this paper studies the exponential stability problem of nonlinear systems. In particular, in [10], by applying the Lyapunov direct approach to the delay-free CFO scenario, the fractional exponential stability (FES), the stability, and the asymptotic stability of nonlinear delay-free CFO systems (CFOSs) were discussed. -E. In [29], [30], Razumikhin-type analysis techniques were used to analyze the effects of delayed impulses on system stability of nonlinear time delay systems. It is a closed subset of the set R of all real numbers. Some sufficient conditions are given to guarantee exponential stability of systems using transition matrix method coupled with dimension expansion technique, where the possibility of the effects of partial unmeasurable states is fully considered. 1). For a given exponentially ABSTRACT. Article MATH Google Scholar Yin J. The exponential stability problem for impulsive systems subject to double state-dependent delays is studied in this paper, where state-dependent delay (SDD) is involved in both continuous dynamics and discrete dynamics and the boundedness of it with respect to states is prior unknown. pth moment exponential input-to-state stability of nonlinear discrete-time impulsive stochastic delay systems. However, [19], [20] had studied the mean square Exponential stability of nonlinear systems with delayed impulses and applications. In this paper, we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems. ) if for every trajectory This paper focuses on the almost sure exponential stability and instability problems for nonlinear stochastic systems. Control. 04. Then in Section 3, several stability theorems on almost sure exponential stability and exponential stability in p th moment, and their corollaries of the given systems are established. By introducing a new method, we obtain some explicit criteria for the practical exponential stability of these equations. A novel exponential stability criterion for the system For example, Li and Yang (2020) derived some sufficient conditions for exponential stability of nonlinear systems with SDD, where the information of the bound of SDD was not needed. Utilizing the average impulsive interval, average impulsive delay, and the Lyapunov method, we present several criteria for p th exponential stability in these systems under a novel condition, diverging from previous This work addresses the global exponential stability of nonlinear delayed discrete-time systems with Markovian switching. A time scale is a model of time. However, an additional restrictive condition on SDD was imposed, namely, it needs satisfy global Lipschitz-like condition, which leads to limited applications. Specifically, the study can be divided into two cases: (1) stability of delayed systems with destabilizing delayed impulses, where the time delays in impulses can be flexible and even larger than the length of impulsive interval, The moment exponential input-to-state stability (ISS) problem for a class of non-linear switched stochastic systems is studied. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete-time nonlinear objects. The global exponential stability and the exponential convergence rate for time-delay systems with nonlinear uncertainties are investigated. Specifically, due to the theory of time-delayed fractional order systems is still not mature, this paper has applied the Laplace transform method and the comparison principle of fractional order differential equation. It is worth noting that the definition of globally weakly This paper studies the stability problem of switched nonlinear homogeneous positive systems in contrast to its non-switched counterparts considered in Aeyels and Leenheer (2002), Bokharaie and Mason (2014), Dong (2015), Feyzmahdavian et al. Exponential stability of switched systems with impulsive effects J. It customizes the classical concept of input-to-state stability (ISS) by imposing exponential convergence rates, ensuring a particular type of exponential decay of the system’s state in the presence of disturbances or inputs. Under certain conditions, we prove such systems have a unique tempered complete quasi-solution which exponentially pullback attracts all solutions starting from a tempered random set. , [7], [12], [15], [16] and the references therein). 10. 1016/j. In this paper, we study the practical exponential stability of nonlinear nonautonomous differential equations under nonlinear perturbations. We address exponential stability of switched nonlinear singular systems with time-delay in which delay is time varying and presents The characterization of the switching signal and the exponential stability of the overall system are carried out simultaneously by using a piecewise Lyapunov functional candidate and linear matrix This paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x(k+1)=Ax(k)+Bx(k−m),k=0,1 The robust stability of nonlinear systems has been studied extensively. Considering technology limitation or device restriction in practical application, we formulate new nonlinear systems with bounded gain error, which contain switched control and impulsive control. Kicha,1,2 M. By means of the stochastic analysis technique and improved Razumikhin method, we obtain several novel stability criteria under the combined action of impulsive disturbance and impulsive control. INTRODUCTION Most systems do not satisfy the principle of linear su-perposition. Crossref View in Scopus Google Scholar [22] Cheng Pei, Deng Feiqi, Yao Fengqi. In contrast with previous works, combining with Lyapunov’s second method and inequalities techniques, two classes of less conservative criteria are obtained, depending on piecewise continuous scalar functions (PCSFs). Based on the impulsive control theory and the ideas of average dwell time (ADT), a set of Lyapunov-based sufficient conditions for globally exponential stability are obtained. This paper considers the absolute exponential stability of switched nonlinear time-delay systems. Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses. Motivated by the aforementioned, in this paper, we will investigate the exponential stability analysis under minimum dwell-time switching for a class of switched non-linear positive systems, whose non-linear function for each subsystem is constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are underlined through some applications concerning 1) exponential stability of nonlinear retarded systems with piecewise constant delays, 2) exponential stability preservation under sampling for semilinear control switching systems, and 3) the link between input-to-state stability and exponential stability of semilinear switching systems. A remarkable method is the switching transformation approach that has been introduced in [19]. Abstract This article addresses the exponential stability problem of switched systems with hybrid delayed impulses that depend on both current states and historical states. In this technical note, we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time-varying disturbances. cityu. Zhu W. Then we By using an average dwell time (ADT) approach that is different from the method in [P. Furthermore, the explicit Request PDF | Exponential Stability of Nonlinear Systems With Delayed Impulses and Applications | We consider a class of nonlinear impulsive systems with delayed impulses, where the time delays in Zhongli You, JinRong Wang, On the exponential stability of nonlinear delay systems with impulses, IMA Journal of Mathematical Control and Information, Volume 35, Issue 3, In this article, we study the representation of solutions and exponential stability of nonlinear impulsive delay systems in the case of commutative matrices. This paper concerns exponential stability of positive nonlinear dynamical systems on time scales. An application to discrete-time neural networks is presented. Given a globally exponentially stable nonlinear stochastic system, the robustness of the global exponential stability of the system subject to a time delay and a neutral term can be derived by a subtle inequality and a transcendental equation. The well-known small-gain theorem implies that a loop-gain of less than unity ensures the stability of dynamical feedback systems. Theorem 1 shows that when the non-linear system without time delay and neutral term is global exponential stable, the non-linear system perturbed by time delay and neutral term may remain to be global The exponential stability problem is considered for a class of nonlinear impulsive and switched time-delay systems with delayed impulse effects by using the method of multiple Lyapunov–Krasovskii functionals. However, we will see in Section 3 that under some Lipschitz assumption on the source term is it possible to ensure a global exponential stability for the L 2 Apart from that, exponential stability problem of time-varying switched nonlinear systems with discrete and distributed delays is addressed through comparison principle in [22]. (2014) and Mason and Verwoerd (2009). Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for stabilizing delayed impulses and destabilizing delayed impulses. tain nonlinear delayed systems and some deﬁnitions are given in Section 2. Research; Open access; Published: 04 October 2018; Exponential stability of nonlinear systems with impulsive effects In the evolution of many real systems, time delays are inevitable and they may have a negative impact on stability of system [10], [11]. Lyapunov was a pioneer in successful endeavors to develop a global approach to the analysis of the stability of nonlinear dynamical systems by comparison with the widely spread This paper investigates the stability problem of partial unmeasurable nonlinear systems under impulsive control. Thence, except for a small part that can be approximately regarded as linear systems, most of This brief is devoted to examine the exponential stability for highly nonlinear hybrid neutral stochastic systems with time varying delays by the novel approach of multiple degenerate functionals. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. 6–8 Particularly, more and more people have paid increasing attention to the Some stability deﬁnitions we consider nonlinear time-invariant system x˙ = f(x), where f : Rn → Rn a point xe ∈ R n is an equilibrium point of the system if f(xe) = 0 xe is an equilibrium point ⇐⇒ x(t) = xe is a trajectory suppose xe is an equilibrium point • system is globally asymptotically stable (G. infinite-dimensional state space, systems is considered. Unlike the previous results, by employing the comparison principle and a method developed in positive systems without involving Lyapunov function, stability criteria are derived under average dwell time (ADT) switching. The time delay is any continuous function belonging to a given interval, but not necessarily differentiable. They ensure that the nonlinear This paper studies the general input-to-state stability problem of the nonlinear delay systems. Nonlinear Dynamics and Systems Theory, 9 (1) (2009) 37–50. For given a switching signal ˙(t), the system (1) is robustly exponentially stable if there exist positive scalars and such that x(t) k’k he (t t 0); t t 0 Some sufficient and necessary conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function, introducing a region of exponential stability. It is shown that, under some conditions, the impulsive synchronization of chaotic systems can be achieved via the input delays in impulses, and design some impulsive controllers that are formalized in terms of linear matrix inequality and ADT-like conditions. Furthermore, in order to describe the convergence rate more accurately, exponential input-to-state stability (EISS) has been proposed. 1 60-66 2005. , negative or positive effects) on system dynamics, namely, it may destroy the stability and lead to Exponential Stability: The origin of ̇x = f (x) is exponentially stable if and only if the linearization of f (x) at the origin is Hurwitz : Let f (x) be a locally Lipschitz function defined over a domain D In this paper, both of Theorem 1 and Theorem 2 solve the exponential stability problem of the nonlinear systems involving partial unmeasurable states under dimension Exponential stability of switched nonlinear systems has been investigated by adopting the linearization method. 272–277 (10. Zhongli You, JinRong Wang, On the exponential stability of nonlinear delay systems with impulses, IMA Journal of Mathematical Control and Information, Volume 35, Issue 3, In this article, we study the representation of solutions and exponential stability of nonlinear impulsive delay systems in the case of commutative matrices. It’s should be highlighted that the above mentioned stability results are asymptotic or exponential. 2012. A novel event-triggered mechanism (ETM) just involving partial known states is desig It is shown that the time delay in impulses exhibits double effects (i. Non-exponential stability and non-exponential stabilization of LTI systems by LTV controllers designed by using solutions to Riccati-type differential equations are presented in [12]. The robust exponential stability problem of the nonlinear impulsive switched systems with switching delays is considered. These results, to the best of our knowledge, are new in the literature and, moreover, cover many previous results on exponential stability of time-delay switched systems. Download PDF. Add to The global exponential stability for a type of continuous-time impulsive switched positive nonlinear systems (ISPNSs) with This paper addresses decentralized exponential stability problem for a class of linear large-scale systems with time-varying delay in interconnection. Different from the previous literature, we aim to show that when the determinate nonlinear delay system is globally exponentially stable, the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable. Generally, even if all the Markovian jump subsystems The asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching and with polynomial growth. This paper is concerned with the problem of practical exponential stability for hybrid impulsive stochastic functional differential systems with delayed impulses, which comprise three classes of systems: the systems with unstable continuous stochastic dynamics and stable discrete dynamics, the systems with stable continuous stochastic dynamics However, little effort has been devoted to highly non-linear switched stochastic systems with non-random switching signals. By utilizing the theory of stochastic analysis, semigroup theory and fixed point theory, a novel sufficient DOI: 10. 2013. Lyapunov stability is named after Aleksandr Mikhailovich Lyapunov, a Russian mathematician who defended the thesis The General Problem of Stability of Motion at Kharkov University in 1892. and Wu Y. Finally, the effectiveness of the proposed criteria is confirmed via an example based on Chua’s oscillator. 2007. However, compared to the abundant theoretical results on global exponential stability (GES) in integer-order differential equations with time delay and impulses, there is a scarcity of research on the exponential stability of conformable fractional-order nonlinear differential systems (CFNDSs) considering both impulse effects and time-varying delay. In Section 4, we study the stability of a special class of system Eq. With two-level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce continuous-time This paper focuses on the almost sure exponential stability and instability problems for nonlinear stochastic systems. The conclusion is given in Section 5. Asymptotic stability in probability and stabilization for a class of discrete-time stochastic systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to uncertainties) local, semi-global, and This paper investigates the exponential stability (ES) of nonlinear discrete-time (DT) systems with stochastic impulses and Markovian jump. This paper considers a class of interconnected nonlinear systems where each subsystem, in the absence of coupling, is individually exponentially stable. Author links open overlay In this section, we will derive sufficient conditions on almost sure exponential stability and th moment exponential stability for such systems. 18. automatica. By means of the above result and In this paper, theoretical investigation has been made on the robustness of global exponential stability of nonlinear systems with deviating argument and stochastic disturbance. II. M. Skip to search form Skip to main content Skip to account menu This study presents new results on the robustness of the global exponential stability of non-linear systems with respect to time delay and neutral term. Two Lyapunov theorems are proposed to check the The practical exponential stability of switched generalized homogeneous positive nonlinear systems with bounded disturbances is investigated in this paper. Article MathSciNet Google Scholar Feyzmahdavian H R, Charalambous T, Johansson M. We prove that impulsive systems, which possess an input-to-state stable (ISS) Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive In this technical note, we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time-varying disturbances. H. L. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied This paper addresses the exponential stability issue of discrete-time switched nonlinear systems by means of the linearization approach. The impulsive switching signals are generated by two types In the paper, we investigate the exponential stability of nonlinear delayed systems with destabilizing and stabilizing delayed impulses, respectively. In contrast with previous works, combining with Lyapunov’s second method and inequalities techniques, two classes of less conservative criteria are obtained, depending on piecewise continuous scalar functions (PCSFs). We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. The second part presents a converse Lyapunov theorem for the notion of semiglobal uniform exponential stability for parametrized nonlinear Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses. By using an improved Lyapunov functional, a sufficient condition for the stability of the systems with being positive is established. The purpose of this paper is to establish the stability criteria for nonlinear Hausdorff dynamical systems. Based on the semi-tensor product of matrices, several sufficient conditions for globally exponential stability are derived. The following theorem will show that if system (2) is globally exponentially stable, system (1) may remain to be globally exponentially stable provided that time This paper deals with a class of uncertain nonlinear impulsive switched systems with time-varying delays. For example, the communication traffic in the networks is usually very large, and the general physical equipment cannot process such a huge amount of data instantaneously, which leads to the delay between signal reception and We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for the practical uniform exponential stability of nonlinear perturbed systems under different conditions for the perturbed term. At each switching time instant, the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems. ‘A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems’, Automatica, 2008, 44, (1), pp. Some less conservative sufficient conditions for uniform exponential stability and uniform practical exponential stability are proposed by In this paper, the problem of globally stochastically exponential stability in the p th moment for a class of T–S fuzzy stochastic impulsive genetic regulatory networks with random discrete delays, distributed delays and parameter uncertainties is discussed. yafzj vyvfe qzeo zbgqr fahlyj xmcxsbh urgkw qdqf vru sin

Exponential stability of nonlinear systems. For a given exponentially … ABSTRACT.