AsymmetricalgebraicRiccatiequation:Ahomeomorphicparametrizationofthesetof solutions

Augusto Ferrante; Michele Pavon; Stefano Pinzoni

doi:10.1016/S0024-3795(01)00241-5

AsymmetricalgebraicRiccatiequation:Ahomeomorphicparametrizationofthesetof solutions

Augusto Ferrante, Michele Pavon, Stefano Pinzoni

Mathematics

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

Abstract

In this paper, asymmetric algebraic Riccati equations are analyzed. In particular, we derive a new parametrization of the set of solutions. Generalizing on the symmetric case, the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related "feedback" matrices. Moreover, the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo-Hamiltonian matrix associated with the equation. We finally show that also the newly introduced parametrization is given by a homeomorphic map.

Original language	English (US)
Pages (from-to)	137-156
Number of pages	20
Journal	Linear Algebra and Its Applications
Volume	329
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(01)00241-5
State	Published - May 15 2001

Keywords

Algebraic Riccati equation
Feedback matrix
Homeomorphism
Invariant subspaces

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(01)00241-5

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abstract = "In this paper, asymmetric algebraic Riccati equations are analyzed. In particular, we derive a new parametrization of the set of solutions. Generalizing on the symmetric case, the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related {"}feedback{"} matrices. Moreover, the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo-Hamiltonian matrix associated with the equation. We finally show that also the newly introduced parametrization is given by a homeomorphic map.",

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author = "Augusto Ferrante and Michele Pavon and Stefano Pinzoni",

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T1 - AsymmetricalgebraicRiccatiequation:Ahomeomorphicparametrizationofthesetof solutions

AU - Ferrante, Augusto

AU - Pavon, Michele

AU - Pinzoni, Stefano

PY - 2001/5/15

Y1 - 2001/5/15

N2 - In this paper, asymmetric algebraic Riccati equations are analyzed. In particular, we derive a new parametrization of the set of solutions. Generalizing on the symmetric case, the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related "feedback" matrices. Moreover, the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo-Hamiltonian matrix associated with the equation. We finally show that also the newly introduced parametrization is given by a homeomorphic map.

AB - In this paper, asymmetric algebraic Riccati equations are analyzed. In particular, we derive a new parametrization of the set of solutions. Generalizing on the symmetric case, the proposed parametrization is obtained in terms of pairs of invariant subspaces of two related "feedback" matrices. Moreover, the connection is clarified between the new parametrization and the classical homeomorphic one based on graph invariant subspaces of the pseudo-Hamiltonian matrix associated with the equation. We finally show that also the newly introduced parametrization is given by a homeomorphic map.

KW - Algebraic Riccati equation

KW - Feedback matrix

KW - Homeomorphism

KW - Invariant subspaces

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VL - 329

SP - 137

EP - 156

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

AsymmetricalgebraicRiccatiequation:Ahomeomorphicparametrizationofthesetof solutions

Abstract

Keywords

ASJC Scopus subject areas

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