Static Output Feedback Control for Discrete-time Piecewise Linear Systems: an LMI Approach

This paper investigates the problem of static output feedback (SOF) control for discrete-time piecewise linear systems. Based on piecewise quadratic Lyapunov functions, new sufficient LMI conditions for the synthesis of SOF stabilization controllers are presented. Meanwhile, by using Finsler's lemma, a set of slack variables with special structure are introduced to reduce design conservatism. Compared to the existing methods, the proposed method has a good performance and can work successfully in situations where the existing methods fail. An extension of this method is also given in order to incorporate H∞ performance. Three examples are given to illustrate the effectiveness of our method.