Non-fragile sliding mode control of discrete switched singular systems with time-varying delays

This study tends to solve the $H_{\infty }$H∞ finite-time boundedness (FTB) problems for discrete switched singular systems with time-varying delays via a non-fragile sliding mode approach. The remarkable feature of the provided method is that a new sliding surface function is constructed such that a full-order dynamic system is acquired. Thus, a non-fragile sliding mode controller can be proposed to guarantee the FTB of the dynamic system. Therein, by employing the multiple Lyapunov-like functions and dwell time (DT) method, sufficient conditions and the DT of switching signal are given to ensure the FTB of the sliding mode dynamics. These results are then applied to the $H_{\infty }$H∞FTB issue, being expressed as a solvable optimisation problem. Furthermore, by employing a discrete reaching condition, the proposed sliding mode controller can guarantee the reachability of the quasi-sliding mode. The validity of the proposed theorems is verified through a numerical example.