LMI Formulation for Static Output Feedback Control of Linear Continuous System

Abstract

In this paper, the static output feedback control of a class of continuous systems is considered. Thanks to the Reciprocal Projection Lemma, it is shown that the solution of the continuous system with static output feedback problem is conditioned by a set of linear matrix inequalities (LMIs), which are numerically tractable and free from any equality constraint. Furthermore, a convex optimization problem with LMI constraint is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop systems. Numerical examples are given to illustrate the effectiveness of the proposed methods.