A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties

This paper proposes a new robust Discrete-Time Sliding Mode Control (DT-SMC) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (UBB) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (LMIs). With respect to that condition a new DT-SMC law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (AUV). The simulation results demonstrate the effectiveness of the proposed controller. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.