Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems

C.R. Kuiper; Heiko J. Zwart

doi:10.1007/BFb0115032

Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In this paper we shall investigate the relation between the eigenvectors of the Hamiltonian and solutions of the Algebraic Riccati Equations (ARE). We restrict ourselves to the case where the Hamiltonian is a Riesz-spectral operator on an infinite-dimensional Hilbert space. We shall present a general form of all possible solutions of the ARE. Conditions for the existence of self-adjoint, nonnegative and stabilizing solutions are given too.

Original language	English
Title of host publication	Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems
Subtitle of host publication	Proceedings of the 10th International Conference, Sophia-Antipolis, France, June 9-12, 1992
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	314-325
Number of pages	12
ISBN (Electronic)	978-3-540-47480-7
DOIs	https://doi.org/10.1007/BFb0115032
Publication status	Published - 14 Jan 1993
Event	10th International Conference on Analysis and Optimization of Systems 1992: State and Freqeuncy Domain Approaches for Infinite-Dimensional Systems - Sophia-Antipolis, France Duration: 9 Jun 1992 → 12 Jun 1992 Conference number: 10

Publication series

Name	Lecture Notes in Control and Information Sciences
Publisher	Springer
ISSN (Print)	0170-8643
ISSN (Electronic)	1610-7411

Conference

Conference	10th International Conference on Analysis and Optimization of Systems 1992
Country/Territory	France
City	Sophia-Antipolis
Period	9/06/92 → 12/06/92

Keywords

Hamiltonian
Algebraic Riccati Equation
infinite-dimensional systems

Access to Document

10.1007/BFb0115032

1 Oral presentation

Solutions of the ARE in terms of Hamiltonian for Riesz-spectral systems
Zwart, H. J. (Speaker)
10 Jun 1992
Activity: Talk or presentation › Oral presentation

1 Report

Solutions of the ARE in terms of the Hamiltonian for Riesz-spectral systems
Kuiper, C. R. & Zwart, H. J., 1992, Enschede: University of Twente. 19 p. (Memorandum; no. 1054)
Research output: Book/Report › Report › Professional

Cite this

Kuiper, C. R., & Zwart, H. J. (1993). Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems. In Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference, Sophia-Antipolis, France, June 9-12, 1992 (pp. 314-325). (Lecture Notes in Control and Information Sciences). Springer. https://doi.org/10.1007/BFb0115032

Kuiper, C.R. ; Zwart, Heiko J. / Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems. Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference, Sophia-Antipolis, France, June 9-12, 1992. Berlin, Heidelberg : Springer, 1993. pp. 314-325 (Lecture Notes in Control and Information Sciences).

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abstract = "In this paper we shall investigate the relation between the eigenvectors of the Hamiltonian and solutions of the Algebraic Riccati Equations (ARE). We restrict ourselves to the case where the Hamiltonian is a Riesz-spectral operator on an infinite-dimensional Hilbert space. We shall present a general form of all possible solutions of the ARE. Conditions for the existence of self-adjoint, nonnegative and stabilizing solutions are given too.",

keywords = "Hamiltonian, Algebraic Riccati Equation, infinite-dimensional systems",

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year = "1993",

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series = "Lecture Notes in Control and Information Sciences",

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pages = "314--325",

booktitle = "Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems",

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note = "10th International Conference on Analysis and Optimization of Systems 1992 : State and Freqeuncy Domain Approaches for Infinite-Dimensional Systems ; Conference date: 09-06-1992 Through 12-06-1992",

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Kuiper, CR & Zwart, HJ 1993, Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems. in Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference, Sophia-Antipolis, France, June 9-12, 1992. Lecture Notes in Control and Information Sciences, Springer, Berlin, Heidelberg, pp. 314-325, 10th International Conference on Analysis and Optimization of Systems 1992, Sophia-Antipolis, France, 9/06/92. https://doi.org/10.1007/BFb0115032

Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems. / Kuiper, C.R.; Zwart, Heiko J.
Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference, Sophia-Antipolis, France, June 9-12, 1992. Berlin, Heidelberg: Springer, 1993. p. 314-325 (Lecture Notes in Control and Information Sciences).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems

AU - Kuiper, C.R.

AU - Zwart, Heiko J.

N1 - Conference code: 10

PY - 1993/1/14

Y1 - 1993/1/14

N2 - In this paper we shall investigate the relation between the eigenvectors of the Hamiltonian and solutions of the Algebraic Riccati Equations (ARE). We restrict ourselves to the case where the Hamiltonian is a Riesz-spectral operator on an infinite-dimensional Hilbert space. We shall present a general form of all possible solutions of the ARE. Conditions for the existence of self-adjoint, nonnegative and stabilizing solutions are given too.

AB - In this paper we shall investigate the relation between the eigenvectors of the Hamiltonian and solutions of the Algebraic Riccati Equations (ARE). We restrict ourselves to the case where the Hamiltonian is a Riesz-spectral operator on an infinite-dimensional Hilbert space. We shall present a general form of all possible solutions of the ARE. Conditions for the existence of self-adjoint, nonnegative and stabilizing solutions are given too.

KW - Hamiltonian

KW - Algebraic Riccati Equation

KW - infinite-dimensional systems

U2 - 10.1007/BFb0115032

DO - 10.1007/BFb0115032

M3 - Conference contribution

T3 - Lecture Notes in Control and Information Sciences

SP - 314

EP - 325

BT - Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems

PB - Springer

CY - Berlin, Heidelberg

T2 - 10th International Conference on Analysis and Optimization of Systems 1992

Y2 - 9 June 1992 through 12 June 1992

ER -

Kuiper CR, Zwart HJ. Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems. In Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems: Proceedings of the 10th International Conference, Sophia-Antipolis, France, June 9-12, 1992. Berlin, Heidelberg: Springer. 1993. p. 314-325. (Lecture Notes in Control and Information Sciences). doi: 10.1007/BFb0115032

Solutions of the ARE in terms of the hamiltonian for Riesz-spectral systems

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Solutions of the ARE in terms of Hamiltonian for Riesz-spectral systems

Research output

Solutions of the ARE in terms of the Hamiltonian for Riesz-spectral systems

Cite this