An LMI approach to sliding mode control design for a class of uncertain time-delay systems

In this paper, the problem of designing sliding mode controls (SMCs) for uncertain time-delay systems is considered. We extend the linear matrix inequality (LMI) approach of Choi [5] to include such systems. Based on the LMI-based method of Choi [5], we get sufficient conditions for the existence of linear sliding surfaces in terms of LMIs, which define convex solution sets, and we show that linear sliding surfaces can be explicitly parameterized using the solution matrices to the LMI existence conditions. We also consider design problems of SMCs guaranteeing a-stability constraint. We give a sufficient condition for the existence of linear sliding surfaces insuring some prescribed decay rate α.