Almost surely exponential stability of mode-dependent stochastic coupled nonlinear systems with semi-Markovian jump

This paper investigates the stability of semi-Markovian jump stochastic coupled nonlinear systems with mode-dependent sojourn time distributions. It is challenging to consider coupling in the semi-Markovian jump systems due to the different networked topologies. First, more realistic complex networks with coupling and semi-Markovian jump are established. Based on Lyapunov method and graph theory, a novel stochastic analysis method and linear comparable Lyapunov like functions are employed to ensure almost surely exponential stability (ASES). Then, without additional restrictions on the sojourn time, the sufficient criterion for ASES is developed. Compared with the most of existing works, which are restrictions on the independence and the distribution function of the sojourn time and the coupling are not considered, our results are meaningful and they can be directly applied to the coupled oscillator model. Finally, some numerical simulations are provided to demonstrate the validity of our results.