Delay-independent minimum dwell time for exponential stability of uncertain switched delay systems

In this technical note, the problem of delay-independent minimum dwell time for exponential stability of uncertain switched delay systems is considered. Piecewise time-varying Lyapunov functionals/functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time-varying delays. This type of delicately constructed Lyapunov functionals/ functions can efficiently eliminate the "jump" phenomena of adjacent Lyapunov functionals/functions at switching times without imposing any restriction on the sizes of time-delays. By applying this type of Lyapunov functionals/functions, it is shown that if each subsystem is delay-independently exponentially stable, then under some conditions there exists a delay-independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time-delays. Two numerical examples are provided to demonstrate the efficiency of the proposed approach.