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

Christopher King; Michael Nathanson

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

Christopher King·Michael Nathanson

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Abstract

Suppose that A and B are real stable 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 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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Christopher King, Michael Nathanson. 2004-03-26. On the existence of a common quadratic Lyapunov function for a rank one difference. https://arxiv.org/abs/math/0403467

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