Input-to-state stability of impulsive stochastic delayed systems under linear assumptions

Wu, Xiaotai; Tang, Yang; Zhang, Wenbing

doi:10.1016/j.automatica.2016.01.002

Cited by 204 publications

(122 citation statements)

References 31 publications

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“…Most of existing results, such as those in [18][19][20][21][22][23][26][27][28][29], are inapplicable to switched system (1). Choose 1 ( , , ) = | | and 2 ( , , ) = (1/2)| | as ISS-Lyapunov functions.…”

Section: Applicationsmentioning

confidence: 99%

“…Roughly speaking, the ISS property means that no matter what the size of the initial state is, the state will eventually approach a neighborhood of the origin whose size is proportional to the magnitude of the input. Many interesting results on ISS properties of various systems such as discrete systems, switched systems, and hybrid systems have been reported; see [18][19][20][21][22][23][24][25][26][27][28][29]. For example, [19] presented converse Lyapunov theorems for input-to-state stability and integral input-tostate stability (iISS) of switched nonlinear systems; [22,23] studied the ISS of nonlinear systems subject to delayed impulses; [29] dealt with the ISS of discrete-time nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

“…For example, [19] presented converse Lyapunov theorems for input-to-state stability and integral input-tostate stability (iISS) of switched nonlinear systems; [22,23] studied the ISS of nonlinear systems subject to delayed impulses; [29] dealt with the ISS of discrete-time nonlinear systems. However, one may observe that most of them, such as those in [18][19][20][21][22][23][24][25][26][27][28][29][30][31], require the derivative of Lyapunov functions to be negative definite in order to derive the desired ISS property. Recently, [32] proposed a new approach for ISS property of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

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Input‐to‐State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Peng

Cao

2018

Complexity

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This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the timederivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

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Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Input‐to‐State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Peng

Cao

2018

Complexity

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“…In the implementation of neural networks, owing to the limited speed of signal propagation, time-varying delays are often encountered. The resulting neural networks with various time delays were extensively studied, and many significant results have been obtained [7,14,17,20,21,35,40,43], see [7,14,43] for discrete time delay, [21] for distributed time delay and [17] for reaction-diffusion delay.…”

Section: Introductionmentioning

confidence: 99%

“…Generally, impulses can affect the dynamical behaviors of the networks, if a network is not stable and the impulsive effects are beneficial to stability, then the network can achieve stability with an appropriate impulsive interval [23,38]. Conversely, if a network is stable and the impulsive effects are harmful to stability, then the impulses may destroy stability [35]. Hence, it is necessary to investigate its influences on the stability of neural networks.…”

Section: Introductionmentioning

confidence: 99%

Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals

Zhang¹,

Zhang²,

Li³

2018

J. Nonlinear Sci. Appl.

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This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval and therefore the proposed impulsive strength-dependent average impulsive interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.

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Stability analysis of Markovian jump systems with delayed impulses

Wang

Ren

2022

Asian Journal of Control

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This paper addresses stability for Markovian jump systems with delayed impulses. The delayed impulse has a largely negative effect on the system stability and is not easy to be studied. The main reason is that so many factors such as Markovian switching, impulse, and time‐varying delay are simultaneously contained and make its analysis complicated and difficult. In order to analyze these factors clearly, some novel enlarging techniques are presented and used to establish linear matrix inequality (LMI) conditions ultimately. Based on the given methods, more situations such as impulsive instant sequence satisfying a renewal process and Poisson process, respectively, are further studied and better than ones without considering such properties. Two numerical examples are used to show the effectiveness and superiority of the methods.

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Input-to-state stability of impulsive stochastic delayed systems under linear assumptions

Cited by 204 publications

References 31 publications

Input‐to‐State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Input‐to‐State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals

Stability analysis of Markovian jump systems with delayed impulses

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