LMI Formulation for Static Output Feedback Design of Discrete-Time Switched Systems

Abstract

This paper concerns static output feedback design of discrete-time linear switched system using switched Lyapunov functions (SLFs). A new characterization of stability for the switched system under arbitrary switching is first given together with 𝛾-performance evaluation. The various conditions are given through a family of LMIs (Linear Matrix Inequalities) parameterized by a scalar variable which offers an additional degree of freedom, enabling, at the expense of a relatively small degree of complexity in the numerical treatment (one line search), to provide better results compared to previous one. The control is defined as a switched static output feedback which guarantees stability and 𝛾-performance for the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed conditions.