Given a stabilizing fixed-order controller, we propose two algorithms which improve its robust stability and robust performance in the framework of the ℋ∞ control problem with constant scaling. The idea is to formulate the scaled ℋ∞ control problem as generalized eigenvalue minimization problems involving (non-linear) matrix inequalities, and then to apply co-ordinate descent algorithms which split the problem into successive (quasi)convex minimization problems. These methods can be considered an extension of the standard μ-synthesis method (the D–K iteration) for fixed-order controller design. Our methods are different from the standard D–K-type iterations in that the analytic centres are computed at each step instead of minimizing objective functions. The controllers obtained may not be globally optimal in general, but are guaranteed to be better than the initial controller. Hence, our methods can be used to improve robustness/performance of a given fixed-order stabilizing controller. Illustrative examples are given for a benchmark problem.
