Stochastic input-to-state stability for stochastic complex dynamical control networks with impulsive perturbation

In this paper, stochastic input-to-state stability (SISS) for stochastic complex dynamical control networks with impulsive perturbation (SCDCNIP) is investigated. An appropriate global Lyapunov function is developed which is closely related to topology of SCDCNIP and dynamical behaviors of every node system of SCDCNIP. Some sufficient criteria are given to guarantee SCDCNIP to meet SISS by imposing the average dwell-time (ADT) condition and reverse average dwell-time (RADT) condition. Moreover, as an application of our theoretical results, typical stochastic coupled oscillators with impulsive perturbation (SCOIP) are studied. Finally, some numerical simulation results are provided to verify the correctness and validity of our results. •We consider some sufficient criteria of SISS for SCDCNIP.•We apply ADT condition, RADT condition, Lyapunov method and stochastic analysis skills.•An application to typical SCOIP is provided.•The effectiveness of results are illustrated with a numerical test.