Dissipativity for a Class of Stochastic Nonlinear Systems With State-Dependent Switching

Dissipativity of stochastic nonlinear systems with state-dependent switching is investigated in this brief. Switching instants are introduced reasonably, based on the evolution of the state trajectory, which are proved to be stopping times. They are the key to apply Itô's formula and Dynkin's formula in stochastic systems. Based on these stopping times, some sufficient conditions on dissipativity of switched stochastic systems are provided. Furthermore, the criteria on global asymptotic stability and input-to-state stability in probability are presented by using a common Lyapunov function technique and multiple Lyapunov functions techniques, respectively. Finally, a numerical example is given to illustrate the validity of our results.