Stabilizing frequency weighted controller reduction approach

This note addresses the problem of instability in frequency weighted controller reduction methods based on similarity transformations. The aim is to reduce the complexity of the controllers derived by modern controller design packages for practical applications. For a given controller a framework is proposed that parameterizes a set of reduced controllers that preserve the stability of the closed loop system. Then based on this result a complementary algorithm to obtain a stabilizing stable reduced controller based on the two sided frequency weighted reduction method is presented. In addition, a sufficient condition for the existence of such a framework is derived.