Riccati Equations on Noncommutative Banach Algebras

Ruth Curtain*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)

Abstract

Conditions for the existence of a solution of a Riccati equation to be in some prescribed noncommutative involutive Banach algebras are given. The Banach algebras are inverse-closed subalgebras of the space of bounded linear operators on some Hilbert space, and the Riccati equation has an exponentially stabilizing solution on this larger space. Applications to spatially distributed systems are given.

Original languageEnglish
Pages (from-to)2542-2557
Number of pages16
JournalSIAM Journal on Control and Optimization
Volume49
Issue number6
DOIs
Publication statusPublished - 2011

Keywords

  • Riccati equations
  • Banach algebras
  • systems over rings
  • optimal control
  • spatially distributed dynamical systems
  • spectral factorization
  • MATRIX ALGEBRAS
  • LINEAR-SYSTEMS

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