Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

Cheng, Pei; Deng, Feiqi; Yao, Fengqi

doi:10.1016/j.nahs.2018.05.003

Cited by 51 publications

(18 citation statements)

References 30 publications

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“…Let the  ∞ -functions 1 (|x|) = ∈ (0, 1); then it follows from Corollary 4 and Theorem 4 that system (32) and (33) are NSS-P with m < − ln = 0.69. The status responses can be shown by Figure 6 when the initial values are chosen as 8, −8, 6, and −10, respectively.…”

Section: Examplementioning

confidence: 99%

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Feng

Park

Zhang

2020

IET Control Theory & Appl

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This paper considers noise‐to‐state stability for random non‐linear systems with stochastic impulses. The impulsive random non‐linear systems contain three random characteristics: the second‐moment processes in continuous dynamics, the sequence of random variables in discrete dynamics, and the number of stochastic impulses obeyed a renewal process. Firstly, the improved criteria of noise‐to‐state stability are established for random non‐linear systems subject to unstable stochastic impulses based on the uniformly asymptotically stable function. Secondly, improved Lyapunov approaches of NSS with unstable stochastic continuous dynamics are accomplished by the uniformly exponentially stable function. Finally, two numerical examples are used to illustrate the feasibility of the proposed methods.

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Section: Examplementioning

confidence: 99%

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Feng

Park

Zhang

2020

IET Control Theory & Appl

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“…Under Assumption 1, it can be easily shown [22][23][24] that there is a unique R n -valued solution x(t) to system (1) on [t 0 , ∞), which is  t adapted and continuous almost surely.…”

Section: Preliminariesmentioning

confidence: 99%

Incremental stability of stochastic time‐varying impulsive and switching systems

Jiao

Zong

Park

et al. 2021

Intl J Robust & Nonlinear

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In this article, the incremental stability problem is addressed for stochastic time‐varying impulsive and switching systems. Both cases of stable continuous subsystems with destabilizing impulses and unstable continuous subsystems with stabilizing impulses are fully considered. By resorting to contraction theory and the Lyapunov function approach together with the dwell time technique, sufficient criteria are established to achieve practical incrementally globally asymptotic stability. Finally, the feasibility of these results is verified by a numerical example.

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“…Stability problems of stochastic systems have also attracted the attention of many researchers. Various stability analysis were made for stochastic delay differential systems (see [29][30][31][32]), impulsive stochastic delay differential systems (see [33][34][35][36][37][38][39]), and impulsive stochastic delay differential systems with markovian switching (see [40,41]), respectively. However, as far as the author knows, there has been no result of stochastic delay system with logic impulses (SDLI), and a SDLI is usually highly complicated to qualitatively analyze due to stochastic effects, delay, logic and impulses exist at the same time.…”

Section: Introductionmentioning

confidence: 99%

Stability of Stochastic Delay Differential Systems With Variable Impulses Due to Logic Choice

2021

IEEE Access

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This paper is concerned with stability problems of stochastic delay differential systems with variable impulses due to logic choice. Firstly, a class of variable impulses due to logic choice is introduced in this paper which is more general than the logic impulses established in [20] and [21]. Then, by establishing a connection between the stochastic delay differential system with logic impulses and a corresponding stochastic delay differential system without logic impulses, some sufficient conditions for stability of the systems are obtained. Finally, the application in a class of linear stochastic delay differential systems with logic impulses is discussed, and several stability criteria together with two numerical examples are given.

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Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

Cited by 51 publications

References 30 publications

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Improved noise‐to‐state stability criteria of random nonlinear systems with stochastic impulses

Incremental stability of stochastic time‐varying impulsive and switching systems

Stability of Stochastic Delay Differential Systems With Variable Impulses Due to Logic Choice

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