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KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2011 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 49, no 2, 464-475 p.Article in journal (Refereed) Published
Abstract [en]

Let R be a commutative complex Banach algebra with the involution .* and suppose that A is an element of R-nxn, B is an element of R-nxm, C is an element of R-pxn. The question of when the Riccati equation PBB*P - PA - A*P - C*C = 0 has a solution P is an element of R-nxn is investigated. A counterexample to a previous result in the literature on this subject is given, followed by sufficient conditions on the data guaranteeing the existence of such a P. Finally, applications to spatially distributed systems are discussed.

Place, publisher, year, edition, pages
2011. Vol. 49, no 2, 464-475 p.
Keyword [en]
Riccati equations, Banach algebras, systems over rings, optimal control, spatially distributed dynamical systems
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-33690DOI: 10.1137/100806011ISI: 000289972200007ScopusID: 2-s2.0-79955668896OAI: diva2:418738
QC 20110524Available from: 2011-05-24 Created: 2011-05-16 Last updated: 2011-05-24Bibliographically approved

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Sasane, Amol
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