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

This paper addresses the problem of delay-dependent robust and reliable <formula><tex>$\mathscr H_\infty $</tex></formula> static output feedback (SOF) control for uncertain discrete-time piecewise-affine (PWA) systems with time-delay and actuator failure in a singular system setup. The Markov chain is applied to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular PWA system. By constructing a mode-dependent piecewise Lyapunov–Krasovskii functional, a new <formula><tex>$\mathscr H_\infty $</tex></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.