Fixed-order H-infinity and H-2 Controller Design for Continuous-time Polytopic Systems: An LMI-based Approach

In this paper, a convex set of fixed-order H-infinity and H2 dynamic output-feedback controllers for continuous-time systems with polytopic uncertainty is proposed. This approach is based on the use of some instrumental stable matrices, which operate as a tool to decouple the controller parameters and the Lyapunov matrices. Then, the stability of the closed-loop system as well as H-infinity and H2 performance criteria are expressed by a set of linear matrix inequalities based upon linearly parameter-dependent Lyapunov matrices. Iterative procedure for updating the instrumental matrices using the previous controller can increase the performance of the approach. Simulation results demonstrate the effectiveness of the proposed method.