Bipartite Synchronization of Stochastic Coupled Systems With Hybrid Time-Varying Delays via Asynchronous Impulsive Control

Abstract

This paper investigates the bipartite synchronization of stochastic coupled systems with hybrid time-varying delays and Markov jump via asynchronous impulsive control. Unlike existing studies, the asynchronous impulses considered in this paper are decentralized, which allows for the investigation of a wider range of dynamic properties. Additionally, to address asynchronous impulsive control, asynchronous average dwell-time condition is introduced for the first time, and new auxiliary functions are defined. Several sufficient criteria for attaining bipartite synchronization are derived through the application of the Lyapunov method and graph theory. In addition, the theoretical findings are applied to single-link robot arms with hybrid time-varying delays. To demonstrate the practicality of the findings, this paper includes two numerical examples.