Reliable Control of Discrete-Time Piecewise-Affine Time-Delay Systems via Output Feedback

This paper addresses the problem of delay-dependent robust and reliable <inline-formula><tex-math notation="LaTeX"> $\mathscr {H}_{\infty }$</tex-math></inline-formula> static output feedback (SOF) control for uncertain discrete-time piecewise-affine (PWA) systems with time-delay and actuator failure in a singular system setup. The Markov chain is applied to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular PWA system. By constructing a mode-dependent piecewise Lyapunov–Krasovskii functional, a new <inline-formula><tex-math notation="LaTeX">$\mathscr {H}_{\infty }$ </tex-math></inline-formula> performance analysis criterion is then presented, where a novel summation inequality and S-procedure are succeedingly employed. Subsequently, thanks to the special structure of the singular system formulation, the PWA SOF controller design is proposed via a convex program. Illustrative examples are finally given to show the efficacy and less conservatism of the presented approach.