H∞ Controller reduction for uncertain systems via rank constrained Linear Matrix Inequalities

We study the H
^infin
Controller reduction problem for structured uncertain systems whose uncertainties are governed by Integral Quadratic Constraints. A sufficient condition for obtaining a reduced-order controller is given in terms of a system of rank constrained Linear Matrix Inequalities which can be solved using existing algorithms. In this approach, the balancing state transformation is a decision variable allowing better performance of the reduced-order controller than the case of a fixed state transformation. The main result is illustrated by two examples.