Finite-time stabilization for a class of nonlinear switched time-delay systems

In this paper, the problem of finite time stabilization is dealt with for a class of switched time-delay systems with nonlinear uncertainties. Firstly, the nonlinear uncertainties are transformed into the linear time-varying forms via the differential mean value theorem (DMVT) under some assumptions. Secondly, by applying the average dwell time method and convexity principle, a finite-time stability condition for the unforced switched time-delay system is established. Then, a state feedback controller is designed which renders the considered system finite-time stable. All the conditions are presented in terms of strict linear matrix inequalities(LMIs), which can be easily checked by using recently developed algorithms in solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the main results.