Quadratic invariance is necessary and sufficient for convexity

In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of of Youla parameters. Previous work has shown that quadratic invariance of the controller set implies...

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Bibliographic Details
Published inProceedings of the 2011 American Control Conference pp. 5360 - 5362
Main Authors Lessard, Laurent, Lall, Sanjay
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2011
Subjects
Aerospace electronics
Complexity theory
Convex functions
Distributed control
Feedback control
Optimization
USA Councils
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ISBN1457700808
9781457700804
ISSN0743-1619
DOI10.1109/ACC.2011.5990928

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Summary:In decentralized control problems, a standard approach is to specify the set of allowable decentralized controllers as a closed subspace of linear operators. This then induces a corresponding set of of Youla parameters. Previous work has shown that quadratic invariance of the controller set implies that the the set of Youla parameters is convex. In this short note, we prove the converse. We thereby show that the only decentralized control problems for which the set of Youla parameters is convex are those which are quadratically invariant.
ISBN:1457700808
9781457700804
ISSN:0743-1619
DOI:10.1109/ACC.2011.5990928