Second-Order Integral Sliding Mode Control for Uncertain Systems With Control Input Time Delay Based on Singular Perturbation Approach

This note proposes a robust integral sliding mode (RISM) manifold and a corresponding design method for stabilization control 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. An improved sliding mode control (SMC), which is delay-dependent and suitable for small input time delay, keeps system stay on the neighborhood of the RISM surface in finite time. With uncertainties and disturbances, the reaching condition for the neighborhood of the RISM is satisfied. Furthermore, the control makes second-order sliding mode. Based on a numerical example, the proposed method is verified to be efficient and feasible.