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A necessary and sufficient minimality condition for uncertain systems

Becker, Carolyn L. and Doyle, John (1999) A necessary and sufficient minimality condition for uncertain systems. IEEE Transactions on Automatic Control, 44 (10). pp. 1802-1813. ISSN 0018-9286. http://resolver.caltech.edu/CaltechAUTHORS:BECieeetac99

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Abstract

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFTs) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well as Kalman-like decomposition structures. A related minimality condition, the converse of the reducibility condition, may then be inferred from these results and the equivalence class of all minimal LFT realizations defined. These results comprise the first stage of a complete generalization of realization theory concepts to uncertain systems. Subsequent results, such as the definition of and rank tests on structured controllability and observability matrices are also given. The minimality results described are applicable to multidimensional system realizations as well as to uncertain systems; connections to formal powers series representations also exist.


Item Type:Article
Additional Information:© Copyright 1999 IEEE. Reprinted with permission. Manuscript received May 9, 1997; revised April 10, 1998. Recommended by Associate Editor, J. Chen.
Subject Keywords:Minimality, model reduction, uncertain systems
Record Number:CaltechAUTHORS:BECieeetac99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BECieeetac99
Alternative URL:http://dx.doi.org/10.1109/9.793720
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1867
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:21 Feb 2006
Last Modified:26 Dec 2012 08:46

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