Hamiltonians and Riccati equations for linear systems with unbounded control and observation operators

C. Wyss; Birgit Jacob; Heiko J. Zwart

doi:10.1137/110839199

Hamiltonians and Riccati equations for linear systems with unbounded control and observation operators

C. Wyss, Birgit Jacob, Heiko J. Zwart

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

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Abstract

In this paper we construct infinitely many selfadjoint solutions of the control algebraic Riccati equation using invariant subspaces of the associated Hamiltonian. We do this under the assumptions that the system operator is normal and has compact inverse and that the Hamiltonian possesses a Riesz basis of invariant subspaces.

Original language	English
Pages (from-to)	1518-1547
Number of pages	30
Journal	SIAM journal on control and optimization
Volume	50
Issue number	3
DOIs	https://doi.org/10.1137/110839199
Publication status	Published - 2012

Keywords

Algebraic Riccati equations
Hamiltonian operator
Infinite-dimensional system
Riescz
Invariant subspace

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10.1137/110839199

Wyss2012hamiltoniansFinal published version, 334 KBLicence: CC BY-NC

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title = "Hamiltonians and Riccati equations for linear systems with unbounded control and observation operators",

abstract = "In this paper we construct infinitely many selfadjoint solutions of the control algebraic Riccati equation using invariant subspaces of the associated Hamiltonian. We do this under the assumptions that the system operator is normal and has compact inverse and that the Hamiltonian possesses a Riesz basis of invariant subspaces.",

keywords = "Algebraic Riccati equations, Hamiltonian operator, Infinite-dimensional system, Riescz, Invariant subspace",

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T1 - Hamiltonians and Riccati equations for linear systems with unbounded control and observation operators

AU - Wyss, C.

AU - Jacob, Birgit

AU - Zwart, Heiko J.

PY - 2012

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AB - In this paper we construct infinitely many selfadjoint solutions of the control algebraic Riccati equation using invariant subspaces of the associated Hamiltonian. We do this under the assumptions that the system operator is normal and has compact inverse and that the Hamiltonian possesses a Riesz basis of invariant subspaces.

KW - Algebraic Riccati equations

KW - Hamiltonian operator

KW - Infinite-dimensional system

KW - Riescz

KW - Invariant subspace

U2 - 10.1137/110839199

DO - 10.1137/110839199

M3 - Article

SN - 0363-0129

VL - 50

SP - 1518

EP - 1547

JO - SIAM journal on control and optimization

JF - SIAM journal on control and optimization

IS - 3

ER -

Hamiltonians and Riccati equations for linear systems with unbounded control and observation operators

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Keywords

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