* Contract grant sponsor: National Science Foundation; contract grant number: YIA award no. ECS-93-58288; contract grant sponsor: GE Foundtion; contract grant sponsor: Boeing. OPTIMAL CONTROL APPLICATIONS & METHODS, VOL. 18, 381—398 (1997) FIXED-ORDER SCALED H  SYNTHESIS TETSUYA IWASAKI * AND MARIO A. ROTEA  Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatsutacho, Midori-ku, Yokohama, Kanagawa 226, Japan  Control Systems Design Laboratory, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, U.S.A. SUMMARY 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 -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 robust- ness/performance of a given fixed-order stabilizing controller. Illustrative examples are given for a bench- mark problem.  1997 John Wiley & Sons, Ltd. Optim. Control Appl. Meth., Vol. 18, 381—398 (1997) (No. of Figures: 4 No. of Tables: 0 No. of References: 37) KEY WORDS: Robust control; H  control; fixed-order control; linear matrix inequality 1. INTRODUCTION Robust stability/performance, of a linear time-invariant system subject to norm-bounded struc- tured uncertainty, can be assessed by computing the scaled H  norm of certain closed-loop transfer matrix.  Minimizing the scaled H  norm of such closed-loop transfer matrix gives rise to a robust synthesis problem that can be used to design controllers; the so-called ‘scaled H  control problem’. In this optimization problem, an optimal scaling matrix as well as an optimal controller are to be found. Global solutions of the scaled H  control problem have been obtained under certain assump- tions on the plant and the scaling set. In the most general case, i.e. output feedback and multivariable plants, the scaled H  control problem remains open. The difficulty is that it is not possible to reparametrize the problem so as to make it have desirable properties such as convexity. As a result, only local solutions (which are not necessarily global) may be found with reasonable amount of computation (see References 11 and 12 for computationally expensive global optimization algorithms). CCC 0143 — 2087/97/060381— 18$17.50 Received 4 December 1996  1997 by John Wiley & Sons, Ltd. Revised 23 September 1996