Stability analysis for stochastic impulsive switched time-delay systems with asynchronous impulses and switches

Abstract

This paper studies stability of a general class of impulsive switched systems under time delays and random disturbances using multiple Lyapunov functions and average dwell-time. In the studied system, impulses and switches are allowed to occur asynchronously. As a result, the switching may occur in impulsive intervals and the impulses could also occur in switching intervals, which affect system stability greatly. Although the switches do no bring about the change of system state, multiple Lyapunov functions do not decrease at the switching times. Therefore, we study two cases: the stable continuous dynamics case and the stable impulsive dynamics case. Based on multiple Lyapunov functions and average dwell-time condition, sufficient stability conditions are derived. Finally, the obtained results are demonstrated through a numerical example from complex switched networks.