Finite-Time Stability of Nonlinear Systems With Delayed Impulses

Finite-time stability (FTS) for nonlinear systems with delayed impulses is characterized in terms of Lyapunov method, where time delays in impulses occur between two consecutive impulse instants. Some Lyapunov-based sufficient conditions are presented to guarantee FTS, where a relationship among the system structure, the delayed impulses, and the settling time is established. For stabilizing impulses with time delays, the design of impulse time sequence is proposed, under which the estimation of settling time relying on the impulse jump, the time delays, and the initial condition is obtained. For destabilizing impulses with time delays, some constraints of the impulse time sequence affected by two different size scopes of time delays are put forward. Our results show that delayed impulses may contribute to or destroy the FTS and lead to different estimations of the settling time. The analysis is illustrated by two numerical examples.