The stability of stochastic coupled systems with time delays and time-varying coupling structure

This paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time-varying coupling structure (SCTVCS). The coupling structure is time-varying first. Second, the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time-varying coupling structure successfully. Combining graph theory with Lyapunov method, a systematic method is given to construct a Lyapunov function for SCTVCS. Several pth moment exponential stability criteria are presented, including a Lyapunov-type theorem, and some sufficient criteria in the form of coefficients. Furthermore, the theoretical conclusions are applied to the stochastic coupled oscillators with time-varying coupling structure, and two stability criteria are obtained. Finally, we give two numerical examples to illustrate the effectiveness of our results.