Finite-time stability and settling-time estimation of nonlinear impulsive systems

This paper studies the problem of finite-time stability (FTS) for nonlinear impulsive systems. Based on impulsive control theory, several Lyapunov-based FTS theorems involving stabilizing impulses and destabilizing impulses are established, respectively. Our proposed results provide sufficient conditions for estimating the settling-time with respect to suitable classes of impulse time sequences. It is shown that the settling-time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect. As compared with the case without using stabilizing impulses, a smaller bound of setting-time can be derived when a FTS system is subject to stabilizing impulses. Conversely, a larger bound of settling-time can be derived when the FTS system is subject to destabilizing impulses, as compared with the case without using destabilizing impulses. As a special case, we extend the ideas to nonlinear impulsive delay systems and derive some delay-independent FTS results. Examples and their simulations are given to demonstrate the applicability of the proposed results.