Robust integral sliding mode control for uncertainsystems with multiple time delays

This paper proposes a robust integral sliding mode (RISM) manifold and the corresponding stabilizationcontrol law for uncertain systems with multiple time-varying time delays based on the techniques of linear matrix inequalities(LMI). The sufficient condition for the existence of the RISM manifold is given in terms of LMI, and then, the slidingmode control (SMC) law that can keep the system state on the RISM manifold from the initial time moment is developed.The efficiency and feasibility of the results are illustrated by a numerical example.