Sliding mode control with delay compensation for uncertain input-delay systems

The paper is concerned with a sliding mode control for the robust stabilization of uncertain input-delay systems with bounded unknown uncertainty. A sliding surface based on a predictor is proposed to minimize the effects of input delay of the system. Then, a robust control law is derived to ensure the existence of a sliding mode and to overcome the delay and the uncertainty of the system in the sliding mode. Because the control input enters the system with a delayed period, uncertainty given at any time is cancelled respectively by the corresponding switching control law after each period of the delay. So the resulting uncertainty can affect the stability the system in the sliding mode in the delay interval. Hence, there is a maximum delay bound such that the system in the sliding mode is globally asymptotically stable. Delay-dependent stability analysis for reduced order dynamics in the sliding mode is employed to estimate the maximum delay bound. A guideline is given for the design of the sliding surface matrix.