Approximation of solutions of Riccati equations

P. Bubák; C.V.M. van der Mee; A.C.M. Ran

doi:10.1137/S0363012903436843

Approximation of solutions of Riccati equations

P. Bubák, C.V.M. van der Mee, A.C.M. Ran

Research output: Contribution to Journal › Article › Academic › peer-review

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. © 2005 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	1419-1435 (electronic)
Journal	SIAM Journal on Control and Optimization
Volume	44
Issue number	4
DOIs	https://doi.org/10.1137/S0363012903436843
Publication status	Published - 2005

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MR2178038

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10.1137/S0363012903436843

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title = "Approximation of solutions of Riccati equations",

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. {\textcopyright} 2005 Society for Industrial and Applied Mathematics.",

author = "P. Bub{\'a}k and {van der Mee}, C.V.M. and A.C.M. Ran",

note = "MR2178038 ",

year = "2005",

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language = "English",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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T1 - Approximation of solutions of Riccati equations

AU - Bubák, P.

AU - van der Mee, C.V.M.

AU - Ran, A.C.M.

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PY - 2005

Y1 - 2005

N2 - 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. © 2005 Society for Industrial and Applied Mathematics.

AB - 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. © 2005 Society for Industrial and Applied Mathematics.

U2 - 10.1137/S0363012903436843

DO - 10.1137/S0363012903436843

M3 - Article

SN - 0363-0129

VL - 44

SP - 1419-1435 (electronic)

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 4

ER -

Approximation of solutions of Riccati equations

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