From LQR to Static Output Feedback: a New LMI Approach

This paper proposes a new Linear Matrix Inequality (LMI) for static output feedback control assuming that a Linear Quadratic Regulator (LQR) has been previously designed for the system. The main idea is to use a quadratic candidate Lyapunov function for the closed-loop system parameterized by the unique positive definite matrix that solves the Riccati equation. A converse result will also be proved guaranteeing the existence of matrices satisfying the LMI if the system is static output feedback stabilizable. The static output feedback includes the LQR solution as a special case when the state is available, which is a desirable property. The examples show that the method is successful and works well in practice.