Static Switched Output Feedback Stabilization for Linear Discrete-time Switched Systems

This paper focuses on the problem of switched static output feedback (SOF) control for discrete-time switched linear systems under arbitrary switching laws. The considered class of systems is characterized by a particular structure of system matrices. Our principle idea is addressed in the derivation of new sufficient linear matrix inequalities conditions for the synthesis of a switched controller for a particular class of switched systems. The adopted methodology is based on the using of a special congruence transformation and a switched quadratic Lyapunov function. We propose important sufficient LMI conditions for SOF stabilization in the general case which guarantee the switchedquadratically stability of the closed-loop system. The various conditions are given through a family of LMI (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 with previous ones in the literature. A numerical example is presented to illustrate the effectiveness of the proposed conditions.