A STRUCTURED APPROXIMATION PROBLEM WITH APPLICATIONS TO FREQUENCY WEIGHTED MODEL-REDUCTION

In this paper we 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 [GRAPHICS] in which each of the R(ij)'s is assumed analytic in the closed right-half plane. If solutions exist, we give a formula for all solutions. Special attention is given to the characterization of all optimal solutions. As an application, we recast the frequency weighted optimal Hankel norm model reduction problem as a problem of characterizing every Q which satisfies a condition of the form [GRAPHICS] in which G is the high-order plant to be approximated and where gamma is to be minimized. After reformulation, the model reduction problem is easily solved using the techniques presented in this paper.