Output feedback controller design for Quadratic Cost Minimization for Linear Systems with Polytopic Uncertainties

This paper proposes a new robust static output feedback control design considering the linear quadratic regulator (LQR) problem based on Linear Matrix Inequalities (LMIs). The output static feedback controller can be used when all the state variables are not available for feedback. This way, the controller design can solve practical problems in which there are no sensors for all state variables of the plant. Furthermore, the presented robust control methodology minimizes an upper bound of a quadratic index (guaranteed cost) related to the output and the control signal of the uncertain closed-loop linear system. Through the designer’s knowledge of the system to be controlled, it is possible to obtain optimized performances. In order to find the best guaranteed cost related to the performance of the system, an algorithm of differential evolution for global optimization was used. The controller was implemented in a bench scale earthquake simulator and the results illustrate the effectiveness of the proposed methodology. In the implementation, a signal fault is assumed, and even in the presence of fault occurrence, the oscillations are attenuated by the proposed robust control.