New Approach to Fixed-Order Output-Feedback Control for Piecewise-Affine Systems

This paper studies the fixed-order piecewise-affine (PWA) output-feedback control of PWA systems in an H∞ setup. In particular, the conventional output-feedback closed-loop system is first augmented with the introduction of the input vector, and a descriptor presentation of PWA system is acquired. Then, a bounded real lemma is derived for the resulting PWA system, which is realized by the construction of a smooth piecewise Lyapunov function and application of the S-procedure. Furthermore, by availing oneself of the descriptor formulation, the fixed-order PWA output-feedback controller synthesis is carried out in a unified framework. An illustrative example is provided to show the efficacy and impact of the proposed control design methodology in a Chua's circuit.