A Structured Approximation Problem with Applications to Frequency Weighted Model Reduction

Keith Glover, David J.N. Limebeer, Y. S. Hung

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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 [formula omitted] in which each of the Rij'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 [formula omitted] in which G is the high-order plant to be approximated and where γ is to be minimized. After reformulation, the model reduction problem is easily solved using the techniques presented in this paper.

Original languageEnglish
Pages (from-to)447-465
Number of pages19
JournalIEEE Transactions on Automatic Control
Issue number4
Publication statusPublished - Apr 1992
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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