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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.

Keywords

Optimization and Control

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/70612

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403467
 http://arxiv.org/abs/math/0403467

Collections

arXiv