Global exponential stability for stochastic coupled systems on networks with Markovian switching

This paper investigates the global exponential stability of stochastic coupled systems on networks with Markovian switching (SCSNMS). Sufficient conditions are established to guarantee p th moment exponential stability and almost surely exponential stability of the SCSNMS, by using concepts from graph theory and M -matrix into Lyapunov method. Consequently, the upper boundaries of the p th moment Lyapunov exponent and the sample Lyapunov exponent are given. Finally, to illustrate the capabilities of the stability principle, easy-verifiable sufficient conditions of global exponential stability for a stochastic coupled oscillator on network with Markovian switching are obtained.