A Robust Sliding Mode Controller for Unmatched Uncertain Severe Sate Time- Delay Systems

This note is concerned with a robust sliding mode control(SMC) for a class of unmatched uncertain system with severe commensurate state time delay. The suggested method is extended to the control of severe state time delay systems with unmatched uncertainties except the matched input matrix uncertainty. A transformed sliding surface is proposed and a stabilizing control input is suggested. The closed loop stability together with the existence condition of the sliding mode on the proposed sliding surface is investigated through one Lemma and two Theorems by using the Lyapunov direct method with the concept of the control Lyapunov function instead of complex Lyapunov-Kravoskii functionals. Through an illustrative example and simulation study, the usefulness of the main results is verified.