Finite-Time Stability of Nonlinear Systems Subject to Impulsive Disturbances

This paper addresses the problem of finite-time stability (FTS) in nonlinear systems subject to impulsive disturbances. It extends and builds upon previous research on impulsive systems. The system under consideration is affected by impulsive disturbances, and is constrained within a more general continuous-time dynamic framework. Based on Lyapunov approach, several FTS conditions with the corresponding settling-time estimations are proposed, where a relationship between the strength of impulsive disturbances, the impulsive interval, and the continuous dynamic is established. Compared with the existing results, the results presented here not only offer broader applicability but also provide more accurate settling-time estimations. Two numerical examples, including one related to finite-time control of spacecraft experiencing impulsive disturbances, are provided together with simulations to show the effectiveness of the presented solutions.