Stability of multi-links complex-valued impulsive stochastic systems with Markovian switching and multiple delays

Yang, Ni; Gao, Ruiyi; Su, Huan

doi:10.1016/j.chaos.2022.112623

Cited by 31 publications

(3 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, the stability of complex networks is an active area of research because it is one of the most fundamental concepts in modern control theory and has wide applications. Therefore, considering the stability analysis of complex networks has important theoretical and applied value [5][6][7][8]. In the real world, numerous systems are often subject to external disturbances, which in most cases were uncertain and treated as random.…”

Section: Introductionmentioning

confidence: 99%

Existence and stability of impulsive stochastic coupled systems in infinite dimensions

Yang

Zhang

2023

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

This paper considers the exponential stability of a class of infinite‐dimensional impulsive stochastic coupled systems. With the help of generalized Itô's formula for the mild solution of infinite‐dimensional systems, we avoid limiting the domain of the mild solution. Then we use the combination of the Lyapunov function and graph theory to construct the Lyapunov function of the systems; the criteria of ‐th moment exponential stability are obtained, which is related to the average impulsive interval and the connectivity of impulsive stochastic systems. In addition, noting that the existence may be affected by impulsive effects and stochastic perturbations, using the graph theory and the principle of contraction mapping, we get the condition that guarantees the existence and uniqueness, which is also related to the structure of the networks. Finally, we consider the stability of impulsive stochastic coupled heat equations and neural networks with reaction diffusion and give some numerical simulations to verify the theoretical results.

show abstract

Section: Introductionmentioning

confidence: 99%

Existence and stability of impulsive stochastic coupled systems in infinite dimensions

Yang

Zhang

2023

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to stabilize a system, external controllers are required. Up to present, many control strategies have been developed, including pinning control, 19,20 impulsive control, 21,22 intermittent control, 10,23 adaptive control 24 and so forth. Notably, controlling all network vertices is not only economically inefficient but also unrealistic in many cases.…”

Section: Introductionmentioning

confidence: 99%

Pinning control for stabilization of coupled stochastic strict‐feedback nonlinear systems

Guo,

Zhao,

2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

This article introduces a novel class of coupled stochastic strict‐feedback nonlinear systems (CSSFNSs) whose topology is not strongly connected. We are devoted to investigating the stabilization issue of CSSFNSs via pinning control. First, the specific form of controllers is decided through the back‐stepping method and the design of virtual controllers. Second, we find a new method to construct the global Lyapunov function of CSSFNS by employing the Lyapunov function of each stochastic strict‐feedback nonlinear system (SSFNS). Meanwhile, combining Lyapunov method with graph theory, several sufficient conditions to guarantee exponential stability in mean square of CSSFNS are obtained in the form of coefficients‐type criterion. Ultimately, our theoretical results are applied to a class of coupled oscillator systems and a predator‐prey model. Furthermore, the validity and feasibility of the theoretical results are illustrated by some numerical simulations.

show abstract

“…Recently, a great many of researchers model this phenomenon by a Markovian switching mechanism, which means that the networks switch from one mode to another one at different time. Up to now, all kinds of related results on stability and synchronization have stirred research interests [12,13,14]. It is worth pointing out that all of above-listed references assume the concerned sojourn-time is governed by the general exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of Semi-Markovian Jumping Uncertain Complex-valued Networks with Time-varying Delay: A Sliding-Mode Control Approach

Li,

Wei,

Hua

2023

Preprint

View full text Add to dashboard Cite

This paper pays close attention to the stabilization issue for delayed uncertain semi-Markovian jumping complex-valued networks via sliding mode control. The concerned corresponding transition rates depend on a positive constant, i.e., sojourn-time, which is not required to obey the general exponential distribution. Combine the generalized Dynkin’s formula with Lyapunov stability theory as well as the characteristics of cumulative distribution functions, a few sufficient criteria are proposed to ascertain the stochastic stability of the obtained sliding mode dynamical system. In addition, design a novel sliding mode controller to ensure all state trajectories of the potential closed-loop system can reach the synthesized sliding mode switching surface in a finite time and maintain there in the subsequent time. In the end of paper, one simple example is presented to verify superiority and feasibility of the provided controller design scheme.

show abstract

Stability of multi-links complex-valued impulsive stochastic systems with Markovian switching and multiple delays

Cited by 31 publications

References 37 publications

Existence and stability of impulsive stochastic coupled systems in infinite dimensions

Existence and stability of impulsive stochastic coupled systems in infinite dimensions

Pinning control for stabilization of coupled stochastic strict‐feedback nonlinear systems

Stabilization of Semi-Markovian Jumping Uncertain Complex-valued Networks with Time-varying Delay: A Sliding-Mode Control Approach

Contact Info

Product

Resources

About