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 |
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Official URL: | http://www.siam.org/journals/sicon.php |

Additional Information: | © 2011 Society for Industrial and Applied Mathematics |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 28 Jul 2011 09:41 |

URL: | http://eprints.lse.ac.uk/37655/ |

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