Robust reduced-order controller synthesis: A dilated LMI approach

This paper develops a new method for the synthesis of robust reduced-order dynamic output feedback controllers for linear time-invariant systems. H₂ and H∞ performance criteria are considered. The method is applicable for both discrete-time and continuous-time systems. The proposed method is based on recently developed extended or dilated linear matrix inequalities (LMIs). A new structure of the slack matrix variables is introduced to obtain an LMI relaxation for the non-convex robust reduced-order controller design problem. The uncertain time-invariant parameters belong to a polytopic domain and affect all the system matrices. Numerical examples demonstrate the effectiveness of the proposed approach.