Robust H∞ Sliding‐Mode Fault‐Tolerant Control for Discrete‐Time Switched Singular Systems With Time‐Delay

ABSTRACT This paper is devoted to addressing the issue of fault‐tolerant control by the design of sliding‐mode control for discrete‐time switched singular systems with time‐delay for arbitrary switching signal. Firstly, the dynamics of the switched sliding‐mode system are determined using a pre‐designed sliding mode surface. Secondly, by using the multiple Lyapunov‐Krasovskii function and Wirtinger‐based integral inequality, less conservative sufficient conditions are derived to ensure the sliding mode dynamics are asymptotically admissible while satisfying a prescribed performance, expressed as linear matrix inequalities. Thirdly, a fault‐tolerant sliding mode control law is synthesized to guide the state trajectories of the system within a bounded sliding‐mode region and to maintain them thereafter. Furthermore, the free weighting matrix technique is employed to introduce an additional degree of freedom, thereby enhancing the conservatism of the suggested approach. Finally, numerical examples are proposed to verify the efficiency and the advantages of the method, along with a comparison of the obtained results to those from previous studies in the literature.