H∞ Static Output Feedback Control for Discrete-time Switched Linear Systems with Average Dwell Time

Abstract—This paper investigates the problem of H∞ static output feedback (SOF) control for discrete-time switched linear systems with average dwell time switching. By using the multiple Lyapunov function technique, a switched SOF controller is designed such that the closed-loop system is exponentially stable and achieves a weighted L2-gain. Sufficient conditions for SOF control are derived and formulated in terms of linear matrix inequalities (LMIs). The minimal average dwell time and the corresponding SOF controller are obtained from the LMI conditions for a given system decay degree. Additionally, based on Finsler’s lemma, two sets of slack variables with special structure are introduced to provide extra freedom in the LMI optimization problem, which leads to reduction of the conservatism and improvement of the performance. A numerical example is given to illustrate the effectiveness of the proposed method.