Incremental stability of stochastic time‐varying impulsive and switching systems

In this article, the incremental stability problem is addressed for stochastic time‐varying impulsive and switching systems. Both cases of stable continuous subsystems with destabilizing impulses and unstable continuous subsystems with stabilizing impulses are fully considered. By resorting to contraction theory and the Lyapunov function approach together with the dwell time technique, sufficient criteria are established to achieve practical incrementally globally asymptotic stability. Finally, the feasibility of these results is verified by a numerical example.