Curtain, Ruth F. and Sasane, Amol J. (2011) On Riccati equations in Banach algebras. SIAM journal on control and optimization (SICON), 49 (2). pp. 464-475. ISSN 0363-0129
Abstract
Let $R$ be a commutative complex Banach algebra with the involution $\cdot^{\star}$ and suppose that $A\in R^{n\times n}$, $B\in R^{n\times m}$, $C\in R^{p\times n}$. The question of when the Riccati equation $PBB^{\star}P-PA-A^{\star}P-C^{\star}C=0$ has a solution $P\in R^{n\times n}$ 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.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.siam.org/journals/sicon.php |
| Additional Information: | © 2011 Society for Industrial and Applied Mathematics |
| Uncontrolled Keywords: | Riccati equations, Banach algebras, systems over rings, optimal control, spatially distributed dynamical systems |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/37655/ |
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