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A Characterization of all Solutions to the Four Block General Distance Problem

Glover, K. and Limebeer, D. J. N. and Doyle, J. C. and Kasenally, E. M. and Safonov, M. G. (1991) A Characterization of all Solutions to the Four Block General Distance Problem. SIAM Journal on Control and Optimization, 29 (2). pp. 283-324. ISSN 0363-0129. doi:10.1137/0329016.

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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.

Item Type:Article
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Doyle, J. C.0000-0002-1828-2486
Additional Information:© 1991 Society for Industrial and Applied Mathematics. Received May 16, 1988. Accepted January 26, 1990.
Subject Keywords:H∞-optimal control, four block problem, Parrott’s theorem, general distance problems, indefinite Riccati equations, indefinite factorization, linear quadratic differential games, Nehari’s theorem
Issue or Number:2
Record Number:CaltechAUTHORS:20120419-081456730
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Official Citation:A Characterization of All Solutions to the Four Block General Distance Problem K. Glover, D. J. N. Limebeer, J. C. Doyle, E. M. Kasenally, and M. G. Safonov SIAM J. Control Optim. 29, pp. 283-324
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30192
Deposited By: Ruth Sustaita
Deposited On:19 Apr 2012 17:25
Last Modified:09 Nov 2021 19:39

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