The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem


Mason, Oliver and Shorten, Robert (2005) The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem. Electronic Journal of Linear Algebra, 12. pp. 42-63. ISSN 1081-3810

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Abstract

In this paper, the structure of several convex cones that arise in the study of Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both linear and non-linear systems are considered, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, some technical results are presented on the structure of individual cones and it is shown how these insights can lead to new results on the problem of common Lyapunov function existence.

Item Type: Article
Keywords: Lyapunov functions and stability; Convex cones; Matrix equations.
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1853
Depositing User: Hamilton Editor
Date Deposited: 22 Feb 2010 12:25
Journal or Publication Title: Electronic Journal of Linear Algebra
Publisher: ILAS - The International Linear Algebra Society
Refereed: Yes
URI:

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