Global stability of coupled nonlinear systems with Markovian switching

This paper investigates the global stability of a coupled nonlinear system with Markovian switching (CNSMS), which can be described in a graph. A theoretical framework for the construction of Lyapunov function for the CNSMS is derived in a combined method of graph theory and Lyapunov function. Furthermore, we obtain a global stochastic asymptotical stability principle, which has a close relation to the topology property of the graph. Finally, to illustrate the capabilities of the principle, the stochastic stability of a coupled oscillator system is investigated.

► We consider some coupled nonlinear systems with Markovian switching.
► We built a framework for the construction of Lyapunov function in graph theory.
► We give some globally stable sufficient conditions.
► These easy conditions relate to the structure of coupling and Markovian switching.