An efficient solution to multi-objective control problems with LMI objectives

We revisit a technique for solving multi-objective control problems through sanely parameterizing the closed-loop system with the Youla parameterizati on and confining the search of the Youla parameter to finite-dimensional su bspaces. It is pretty well-known how to solve such problems if the closed-l oop specifications are formulated in terms of the solvability of linear mat rix inequalities. However, all. approaches proposed so far suffer from a su bstantial inflation of size of the resulting optimization problems if impro ving the approximation accuracy. On the basis of a novel state-space approa ch to solving static output feedback control problems by convex optimizatio n for a specific class of plants, we reveal how the growth of the size of t he optimization problems can be considerably reduced to arrive at more effi cient algorithms. As an additional ingredient we discuss how to use the so- called mixed controller as a starting point for a genuine multi-objective d esign in order to improve the algorithms. (C) 2000 Elsevier Science B.V. Al l rights reserved.