Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems

Ai, Zidong; Zong, Guangdeng

doi:10.1016/j.amc.2014.07.092

Cited by 45 publications

(32 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10,11 However, the existing researches are mostly confined the switched systems only driven by pure-diffusion Brownian motion. [6][7][8][9][10][11][12] Compared with Brownian motion, jump-diffusion Lévy process allows the sample paths to not only continuously fluctuate at most of the time but also exhibit sudden jumps occasionally 13 . Due to the merits of Lévy process, Lévy noise as formal derivative of Lévy process has been widely used in various applications including mathematical finance, quantum physics, and mathematical biology.…”

Section: Introductionmentioning

confidence: 99%

An averaging principle for stochastic switched systems with Lé vy noise

Kang

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we present an averaging method for stochastic switched systems with L é vy noise under non‐Lipschitz condition. With the help of successive approximation method and Bihari's inequality, the existence and uniqueness of the solutions of original and averaged systems are proved. Then, under suitable assumptions, we show that the solution of stochastic switched system with L é vy noise strongly converges to the solution of the corresponding averaged equation.

show abstract

Section: Introductionmentioning

confidence: 99%

An averaging principle for stochastic switched systems with Lé vy noise

Kang

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…ISS property analysis of nonlinear systems with disturbance inputs is one of active research topics in modern nonlinear control theory. Therefore, it is of great significance to study ISS for impulsive systems, see, eg, other works …”

Section: Introductionmentioning

confidence: 99%

“…Most of the existing results pertain to the study of ISS property for continuous‐time impulsive systems, see other works and the references therein, but fewer studies the ISS property for discrete‐time impulsive systems . In addition, time delays occur frequently in many real‐world phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, many systems in the real world may be disturbed by stochastic factors. In the past decades, there has been an increasing interest in the ISS property analysis of continuous‐time stochastic impulsive systems, see other works and the references therein. In the work of Wu et al, by means of the Lyapunov‐Krasovskii functional and the average impulsive interval approach, the ISS, integral‐ISS, and stochastic‐ISS for continuous‐time impulsive stochastic delayed systems are considered under linear assumptions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary This paper investigates the pth moment exponential input‐to‐state stability (ISS) of nonlinear discrete‐time impulsive stochastic delay systems. By employing Lyapunov functionals, some pth moment exponential ISS criteria are provided. The obtained results show that a discrete‐time stochastic delay system can become pth moment exponential input‐to‐state stable by impulsive controls even if it may be not input‐to‐state stable itself. On the other hand, the original system without impulses can retain its ISS property with appropriate destabilizing impulses. As an application, the theoretical results are used to test the ISS for a class of recurrent neural networks under stochastic perturbations. Finally, a numerical example is presented to illustrate the effectiveness of the results.

show abstract

“…Recently, some efforts have been made to extend the stability results from stochastic systems to stochastic switched systems (Feng and Zhang 2006; Feng et al. 2011; Chatterjee and Liberzon 2004; Filipovic 2009; Ai and Zong 2014). In Branicky (1998), Dimarogonas and Kyriakopoulos (2004) and Chatterjee and Liberzon (2006) the investigators utilize multiple Lyapunov functions approach to study the stability of stochastic switched systems.…”

Section: Introductionmentioning

confidence: 99%

P-th moment and almost sure stability of stochastic switched nonlinear systems

Gao

2016

SpringerPlus

View full text Add to dashboard Cite

This paper mainly tends to utilize -type function to investigate p-th moment and almost sure stability for a class of stochastic switched nonlinear systems. Based on the multiple Lyapunov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the proposed results.

show abstract

Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems

Cited by 45 publications

References 19 publications

An averaging principle for stochastic switched systems with Lé vy noise

An averaging principle for stochastic switched systems with Lé vy noise

pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

P-th moment and almost sure stability of stochastic switched nonlinear systems

Contact Info

Product

Resources

About