Some control problems can be formulated as convex problems involving linear matrix inequalities, Not only controllers for linear time invariant systems can be designed in this way but also controllers for linear systems with time varying uncertainties. It is also possible to design reduced order controllers, but the problem is no longer convex. To design a controller of the lowest possible order that satisfies the constraints, the minimal rank of an affine matrix function has to be found subject to linear matrix inequalities. In this paper an algorithm is proposed for solving such problems. It is an extension of a potential reduction method for solving convex optimization problems. The problem of finding minimum rank solutions is, however, not convex. Still, with the proposed potential reduction method reduced rank solutions can easily be obtained.
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