Approximation of solutions of Riccati equations

P. BUBAK;VAN DER MEE, CORNELIS VICTOR MARIA;A. C. M. RAN

2005-01-01

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Abstract

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second is approximation of the solution of the algebraic Riccati equation by finite dimensional approximants. The theory of exponentially dichotomous operators and bisemigroups is instrumental in our approach.