Exponential stabilization using sliding mode control for non linear systems with time-varying delays

This paper deals with exponential stabilization of linear systems with delay using a state feedback sliding mode controller. The approach is based on Lyapunov-Krasovskii techniques and uses a descriptor representation. The exponential stability properties are proved using an appropriate change of variables associated with a polytopic representation. The system under consideration is subject to unknown, time-varying but bounded delays. The results are given in terms of LMIs. An example is given to show the efficacy of the approach.