Stability Analysis Of Stochastic Impulsive Switched Systems With Deterministic State-Dependent Impulses And Switches

This paper studies stability of stochastic impulsive switched systems with deterministic state-dependent impulses and switches. Here, "deterministic state-dependent" means that both switching and impulsive rules are deterministic and related to system states. Since impulses and switches are not necessarily synchronous, we first investigate stochastic impulsive switched systems with asynchronous time-dependent impulses and switches. Both the existence and convergence of the system solution are studied, and stability conditions are derived via the tradeoff between two average dwell-times for switching and impulsive time sequences. For the state-dependent case, based on active regions for the switching and assigned regions for the impulses, we first develop impulsive and switching rules such that both impulsive and switching times are stopping times, then verify the existence and uniqueness of the system solution, and finally establish stability conditions. Furthermore, we discuss the combination of time-dependent and state-dependent cases, and investigate the quasi solution of the system to relax the assumption on active regions. Finally, two numerical examples are presented to illustrate the derived results.