Integral sliding mode control for uncertain systems with input delay based on singular perturbation approach

This paper proposes a robust integral sliding mode (RISM) manifold and the corresponding design method of stabilization control law for uncertain systems with control input time delay. Delay-independent sufficient condition for the existence of the RISM surface is given in terms of LMI, and the sliding mode control (SMC) law which can keep system stay on the neighborhood of the RISM surface in finite time is developed based on singular perturbation approach. With uncertainties and disturbances, the reaching condition for the neighborhood of the RISM is also satisfied, and the final control makes second-order sliding mode. Based on a numerical example, the proposed method is verified to be efficient and feasible.