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On the existence of a common quadratic Lyapunov function for a rank one difference

✍ Scribed by Christopher King; Michael Nathanson

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 213 KB
Volume: 419
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.05.010

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✦ Synopsis

Suppose that A and B are real Hurwitz matrices, and that their difference A -B is rank one. Then A and B have a common quadratic Lyapunov function if and only if the product AB has no real negative eigenvalue. This result is due to Shorten and Narendra, who showed that it follows as a consequence of the Kalman-Yacubovich-Popov lemma and the solution of the Lur'e problem. Here we present a new and independent proof based on results from convex analysis and the theory of moments.

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