Exponential admissibility for singular systems with time-varying delay by sliding mode control

This paper deals with the problem of sliding mode control (SMC) for a class of singular systems with time-varying delay. A sliding mode controller is designed such that the singular system is exponentially admissible and in finite time the trajectory of singular system can be driven onto the sliding surface. By constructing a Lyapunov-Krasovskii functional and using the free-weighting matrix approach, the results on exponential stabilization are obtained in terms of strict linear matrix inequalities (LMIs). The derivative of the time-varying delay does not require to be smaller than one is a advantage of this paper. Finally, the effectiveness of the proposed main results is illustrated by a numerical example.