Characterization of all solutions to the four block general distance problem

K. Glover, D. J.N. Limebeer, J. C. Doyles, E. M. Kasenally, M. G. Safonov

Research output: Contribution to journalArticlepeer-review

136 Citations (Scopus)

Abstract

All solutions to the four block general distance problem which arises in H optimal control are characterized. The procedure is to embed the original problem in an all-pass matrix which is constructed. It is then shown that part of this all-pass matrix acts as a generator of all solutions. Special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all-pass transfer functions. As an application, necessary and sufficient conditions are found for the existence of an H optimal controller. Following that, a descriptor representation of all solutions is derived.

Original languageEnglish
Pages (from-to)283-324
Number of pages42
JournalSIAM Journal on Control and Optimization
Volume29
Issue number2
DOIs
Publication statusPublished - 1991
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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