# On Riccati equations in Banach algebras

Curtain, Ruth F. and Sasane, Amol J. (2011) On Riccati equations in Banach algebras. SIAM Journal on Control and Optimization, 49 (2). pp. 464-475. ISSN 0363-0129

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Identification Number: 10.1137/100806011

## 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 http://www.siam.org/journals/sicon.php © 2011 Society for Industrial and Applied Mathematics Q Science > QA Mathematics Departments > Mathematics 28 Jul 2011 09:41 25 Oct 2017 08:43 http://eprints.lse.ac.uk/id/eprint/37655