A structured approximation problem with applications to frequency weighted model reduction

The authors consider the problem of finding necessary and sufficient conditions for the existence of a Q with no more than k poles in the closed left-half plane such that the norm of a certain matrix ≤ 1. If solutions exist, a formula for all solutions is given. Special attention is given to the characterization of all optimal solutions. As an application, the frequency weighted optimal Hankel norm model reduction problem is recast as a problem of characterizing every Q which satisfies a certain condition. After reformulation, the model reduction problem is easily solved using the techniques presented in this work.link_to_subscribed_fulltex