Stability and Control Design of Stochastic Dynamical Systems with Impulses

This paper is concerned with the stability and performance of hybrid stochastic dynamic systems (HSDS). The objective is to examine a general form of HSDS thereby providing sufficient conditions to guarantee bounded stability or mean square stability and to investigate the behavior based on a prescribed level of Hperformance for linear HSDS. We establish improved sufficient conditions for bounded stochastic stability of continuous impulsive systems, which are only stable outside a certain ball containing the equilibrium point. This leads to the result that the continuous stochastic flow dynamics is stable everywhere but the impulsive dynamics could be unstable everywhere. Relevant results are derived for the case that both the impulsive and the continuous dynamics are stable. Simulation studies are provided to demonstrate the usefulness of the proposed theory.