Finite-Time Stability of Impulsive and Switched Hybrid Systems With Delay-Dependent Impulses

This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems. When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently. When switching dynamics may not be FTS and impulsive dynamics involve stabilizing delay-dependent impulses, the uninterrupted impulses can achieve the FTS of hybrid system. Moreover, the STF presents a class of uniformity about the impulsive and switching hybrid signals. The analysis is illustrated by a practical example.