ON RICCATI EQUATIONS IN BANACH ALGEBRAS
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
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.
Riccati equations, Banach algebras, systems over rings, optimal control, spatially distributed dynamical systems
IdentifiersURN: urn:nbn:se:kth:diva-33690DOI: 10.1137/100806011ISI: 000289972200007ScopusID: 2-s2.0-79955668896OAI: oai:DiVA.org:kth-33690DiVA: diva2:418738
QC 201105242011-05-242011-05-162011-05-24Bibliographically approved