Synchronization of Hybrid Stochastic Coupled Systems With Semi‐Markov Jump and Time‐Varying Delays Via Adaptive Aperiodically Intermittent Control

ABSTRACT In this article, the synchronization problem of hybrid stochastic coupled systems with semi‐Markov jump and time‐varying delays via adaptive aperiodically intermittent control is studied, which satisfies the nonlinear coupling condition. Compared with the existing works on hybrid coupling, the hybrid coupling in this paper is not limited to linear coupling conditions. Additionally, the model incorporates time‐varying delays, stochastic perturbations, and semi‐Markov jump topology to enhance its generality. It is worth noting that addressing the combined effects of these factors to achieve synchronization poses significant challenges. Through the Lyapunov method and graph theory, some sufficient conditions for adaptive aperiodically intermittent controller are obtained. Furthermore, several synchronization criteria related to the system's topology and the maximum uncontrolled ratio are established. Finally, an illustrative example is given to show the effectiveness and applicability of the theoretical results.