An LMI formulation of fixed-order H∞ and H2 controller design for discrete-time systems with polytopic uncertainty

In this paper, a new approach to fixed-order H_∞ and H₂ output feedback control of MIMO discrete-time systems with polytopic uncertainty is proposed. The main idea of this approach is based on the definition of SPR-pair matrices and the use of some instrumental matrices which operates as a tool to overcome the original non-convexity of fixed-order controller design. Then, stability condition as well as H_∞ and H₂ performance constraints are presented by a set of linear matrix inequalities with linearly parameter dependent Lyapunov matrices. An iterative algorithm for update on the instrumental matrices is developed, that monotonically converges to a suboptimal solution. Simulation results show the effectiveness of the proposed approach.