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Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation

Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation
Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation
We study the existence of positive and negative semidefinite solutions of algebraic Riccati equations (ARE) corresponding to linear quadratic problems with an indefinite cost functional. The problem to formulate reasonable necessary and sufficient conditions for the existence of such solutions is a long-standing open problem. A central role is played by certain two-variable polynomial matrices associated with the ARE. Our main result characterizes all unmixed solutions of the ARE in terms of the Pick matrices associated with these two-variable polynomial matrices. As a corollary of this result we obtain that the signatures of the extremal solutions of the ARE are determined by the signatures of particular Pick matrices.
969-991
Trentelman, Harry L.
28ee0a03-4052-46ce-8e7e-41f6a76fe450
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Trentelman, Harry L.
28ee0a03-4052-46ce-8e7e-41f6a76fe450
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b

Trentelman, Harry L. and Rapisarda, Paolo (2001) Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation. SIAM Journal on Control and Optimization, 40 (3), 969-991.

Record type: Article

Abstract

We study the existence of positive and negative semidefinite solutions of algebraic Riccati equations (ARE) corresponding to linear quadratic problems with an indefinite cost functional. The problem to formulate reasonable necessary and sufficient conditions for the existence of such solutions is a long-standing open problem. A central role is played by certain two-variable polynomial matrices associated with the ARE. Our main result characterizes all unmixed solutions of the ARE in terms of the Pick matrices associated with these two-variable polynomial matrices. As a corollary of this result we obtain that the signatures of the extremal solutions of the ARE are determined by the signatures of particular Pick matrices.

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Published date: 2001
Organisations: Southampton Wireless Group

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Local EPrints ID: 262216
URI: http://eprints.soton.ac.uk/id/eprint/262216
PURE UUID: 73e6d7b8-6c12-4b7d-8912-a12ccfb52387

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Date deposited: 30 Mar 2006
Last modified: 19 Jul 2019 22:32

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Contributors

Author: Harry L. Trentelman
Author: Paolo Rapisarda

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