Sliding mode control for linear systems with time-varying input and state delays

This paper deals with a sliding mode control for linear systems with input and state time-varying delays. Two different time delays are considered for the sliding mode control of a continuous linear system. Delay-dependent sufficient conditions are given for the existence of sliding manifolds in terms of linear matrix inequalities. A reaching motion controller is also proposed for such systems by means of both reaching law and inequality approach. An inverted pendulum system is utilized to illustrate the effectiveness of the developed techniques.