ON RICCATI EQUATIONS IN BANACH ALGEBRAS

被引：10

作者：

Curtain, Ruth ^{[1
]}

Sasane, Amol ^{[2
]}

机构：

[1] Univ Groningen, Dept Math, NL-9700 AV Groningen, Netherlands

[2] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2011年 / 49卷 / 02期

关键词：

Riccati equations; Banach algebras; systems over rings; optimal control; spatially distributed dynamical systems;

D O I：

10.1137/100806011

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：464 / 475

页数：12

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