Synchronization for Coupled Stochastic Nonlinear Systems With Time-Varying and Non-Strongly Connected Structure

This article studies the synchronization problem in a class of coupled stochastic nonlinear systems featuring time-varying and non-strongly connected coupling structures. In order to solve the problem posed by non-strong connectivity, an innovative hierarchical method is proposed, which enables us to study the synchronization in a layered manner. For achieving synchronization, actual controllers are constructed through the application of new coordinate transformations and the design of virtual controllers. Furthermore, by leveraging graph theory techniques and Lyapunov method, the mean square exponential synchronization criterion is derived. Finally, the theoretical results are applied to coupled Chua’s circuits, and their effectiveness is confirmed via numerical simulations. Note to Practitioners—This article is motivated by the synchronization results of stochastic strict-feedback nonlinear systems. At present, most studies concentrate on simple single-input single-output stochastic nonlinear systems, yet interconnected multi-input multi-output stochastic nonlinear systems hold greater significance in real-world scenarios. This research expands its focus to the coupling structures between interconnected stochastic nonlinear systems, which are not only time-varying but also allow non-strongly connected topological forms. This extension significantly enhances the practical application of traditional single-input single-output nonlinear systems. Additionally, considering the non-strongly connected nature, an innovative hierarchical approach is proposed. This method allows for layer-by-layer synchronization analysis, concurrently broadening the application of graph theory in this field. In the process of ensuring the synchronization of each layer, successful construction of fourth-order Lyapunov functions and actual controllers was achieved through appropriate variable substitutions and virtual controllers design. Overall, this paper provides a new perspective and methodology for the synchronization analysis and research of interconnected stochastic nonlinear systems.