Robust State Feedback Design for Uncertain Systems Based on Luenberger Observer

Abstract

This paper proposes a robust state feedback design method based on a new Luenberger observer for uncertain systems with measurement output matrices containing uncertain parameters. First, in view of the problem that it is challenging to measure state variables in practice, an observer is designed through the feedback of the observation state. Considering the situation that the measurement output matrix contains uncertain parameters in the uncertain system, a new Luenberger observer is designed. Then, based on the new Luenberger observer, and combined with the multi-affine representation and the slack variable framework, the convex linear matrix inequality condition related to the Lyapunov function is obtained, and the robust stability analysis based on linear matrix inequalities is conducted for the closed-loop system. Finally, the feasibility of the above condition is tested by an experiment to show the applicability and effectiveness of the proposed method.

Keywords

• uncertain systems
• luenberger observer
• multi-affine representations
• robust design
• observed-state