Finite-Time Stability of Switched Nonlinear Systems With State Jumps: A Dwell-Time Method

Abstract

This article investigates the finite-time stability (FTS) of switched nonlinear systems (SNSs) with state jumps. Our main concerns are twofold. One is that the SNS only consists of FTS subsystems. The other is that the SNS has both FTS subsystems and exponentially stable (ES) subsystems. Due to the switches and state jumps, the main challenge of the study comes from the estimation of settling time and the synthesis of different Lyapunov functions for FTS/ES subsystems. Based on the analytical-inductive method and the initial-value-dependent dwell-time approach, several FTS criteria for the SNSs are established. Then, we provide the estimation of settling time which is explicitly dependent on the dwell time and initial value. Our results can be applied to the finite-time control problem of switched systems with/without state jumps, even when some subsystems can only be exponentially stabilized through linear feedback control and others are finite-time stabilized by discontinuous/nonlinear controls. Finally, three examples are given to illustrate the proposed results. The finite-time stabilization of a continuous stirred tank reactor and the finite-time consensus of a multiagent system are both adopted as potential applications.