Fixed-Order H∞ Controller Design for Systems with Polytopic Uncertainty

Abstract

AbstractThis note provides sufficient conditions for fixed-order H∞ controller design for SISO systems with polytopic uncertainty. New conditions are derived based on the concept of robust strict positive realness of an uncertain polynomial with respect to a parameter dependent polynomial. The main feature of the proposed method is that the non-convex set of fixed-order stabilizing controllers is approximated with an inner set which is not necessarily a convex set. The quality of this approximation depends on an initial stabilizing controller. The proposed conditions are in terms of solution to a set of linear matrix inequalities. The effectiveness of the proposed approach is demonstrated by comparing with the existing results.