Fixed-order H∞ and H2 controller design for continuous-time polytopic systems: An LMI-based approach

In this paper, a new approach for fixed-order H_∞ and H₂ dynamic output-feedback controller design of continuous-time systems with state space polytopic uncertainty is proposed. This approach is based on the use of some instrumental matrices, which operate as a tool to decouple the controller parameters and the Lyapunov matrices. The stability of the closed-loop system as well as H_∞ 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.