Reliable Output Feedback Control for Piecewise Affine Systems With Markov-Type Sensor Failure

This brief addresses the problem of 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 sensor failure in a descriptor system framework. The Markov chain is employed to describe the sensor failure behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is initially converted into a descriptor PWA model. On the basis of a mode-dependent piecewise Lyapunov function, combined with S-procedure, a novel <inline-formula> <tex-math notation="LaTeX">${\mathscr {H}_{\infty }}$ </tex-math></inline-formula> performance analysis criterion is then presented. Furthermore, by some elegant linearization techniques, the PWA SOF controller design is proposed in terms of the feasibility of a convex optimization problem. Lastly, a numerical example illustrates the effectiveness and less conservatism of the proposed approach.