Exponential stability for stochastic systems with hysteresis switching

For stochastic switched systems, the exponential stability is considered in this paper. To construct the solution of the switched system, we only focus on the hysteresis switching rule which is state-dependent and can be viewed as a closed-loop control scheme. Compared with the existing methods, the main difficulty comes from how to apply Dynkin´s formula and exponential martingale inequality to the case where locally Lipschitz conditions are destroyed by switching behaviors. The criteria on moment exponential stability and almost sure exponential stability are extended to stochastic systems with hysteresis switching. The simulation example demonstrates that unstable individual systems can be switched to an exponentially stable hybrid system.