Lyapunov Conditions for Stability of Stochastic Impulsive Switched Systems

This paper studies stability of stochastic impulsive switched systems. Different from exponential Lyapunov function and average dwell-time in the previous works, general Lyapunov function and fixed dwell-time are implemented in this paper to analyze input-to-state stability and global stability of stochastic impulsive switched systems. Two cases are investigated, that is, the case that the continuous dynamics is stable and the case that the discrete dynamics is stable. To implement multiple Lyapunov functions, there are two subcases considered in this paper: the subcase that the estimates on the derivatives of the multiple Lyapunov functions are the same and the subcase that the growths of the multiple Lyapunov functions by the jumps are the same. For aforementioned different cases, sufficient stability conditions are established for stochastic impulsive switched systems. Finally, the developed theory is illustrated through examples from networked control systems and synchronization problem of 3-D novel chaotic circuit systems.