Stochastic Stability of Impulsive Switched Systems With Constrained Switching and Impulses

This letter studies stochastic stability for impulsive switched systems with constrained switching and impulses. Here, “constrained” means that at each discrete-time instant, the switching and impulse are limited in a subset of all the modes. Constrained switching and impulses exist widely in many physical systems due to limitations on system structures and information transmission. Under constrained switching and impulses, we investigate stochastic stability of impulsive switched systems in three cases. For each case, stability conditions are derived using multiple Lyapunov functions and mode-dependent average dwell-time, and thus relax the conservatisms caused by common Lyapunov function and average dwell-time. Finally, two numerical examples are given to illustrate the obtained results.