A further step to transient performance enhancement of discrete-time singular systems with time-varying delay

This paper is the first attempt to enhance the transient performance while simultaneously addressing the output regulation challenges for discrete singular time-delay systems subject to actuator saturation. The proposed controller consists of two linear and nonlinear parts, without any switching elements. The linear part is designed to solve the main regulation problem, while the nonlinear part is designed to enhance the performance of the closed-loop system in the face of input saturation. The delay-range dependent stability conditions of the closed-loop system are analysed using the Lyapunov-Krasovskii (LK) approach, which involves solving an LMI problem to determine the parameters of the proposed controller. Furthermore, the admissibility of the closed-loop system is assessed to ensure the system's stability, regularity, and causality. Finally, the theoretical achievements are endorsed by simulations through numerical and practical examples.