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On the solvability for the mixed-type Lyapunov equation

On the solvability for the mixed-type Lyapunov equation In this paper, the linear matrix equation X = AXB* + BXA* + Q is considered, which is called the mixed-type Lyapunov equation. Some necessary and sufficient conditions for the existence of a unique solution are presented. Since a Hermitian positive semidefinite solution is important from the application point of view, some sufficient conditions for the existence of a Hermitian positive semidefinite solution are derived. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png IMA Journal of Applied Mathematics Oxford University Press

On the solvability for the mixed-type Lyapunov equation

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Publisher
Oxford University Press
Copyright
© The Author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
ISSN
0272-4960
eISSN
1464-3634
DOI
10.1093/imamat/hxh099
Publisher site
See Article on Publisher Site

Abstract

In this paper, the linear matrix equation X = AXB* + BXA* + Q is considered, which is called the mixed-type Lyapunov equation. Some necessary and sufficient conditions for the existence of a unique solution are presented. Since a Hermitian positive semidefinite solution is important from the application point of view, some sufficient conditions for the existence of a Hermitian positive semidefinite solution are derived.

Journal

IMA Journal of Applied Mathematics – Oxford University Press

Published: Apr 1, 2006

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