New Finite-time Stability and Boundedness Conditions for Time-Delay Switched Linear Systems with Finite-Time Unstable and Unbounded Subsystems

In this paper, finite-time stability and finite-time boundedness of a class of switched delay systems with subsystems which are not finite-time stable and finite-time bounded is investigated. Based on Lyapunov-Krasovskii functional technique and the average dwell time approach new delay-dependent criteria which guarantee finite-time stability and finite-time boundedness of time-delay switched linear systems is proposed. In other words, the obtained necessary and sufficient conditions guarantee finite-time stability and finite-time boundedness of linear switched delay systems while some subsystems are not finite-time stable and finite-time bounded. Finally, simulation results are provided to show the effectiveness of the proposed method. The numerical results illustrate the effect of switching signals and the total dwell time of finite-time unstable and finite-time unbounded subsystems on finite-time stability and finite-time boundedness of time-delay switched linear systems.