Journal Article

Can we prove stability by using a positive definite function with non sign-definite derivative?

Iasson Karafyllis

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 2, pages 147-170
Published in print June 2012 | ISSN: 0265-0754
Published online November 2011 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnr035
Can we prove stability by using a positive definite function with non sign-definite derivative?

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Novel criteria for global asymptotic stability are presented. The results are obtained by a combination of the ‘discretization approach’ and the ideas contained in the proof of the original Matrosov's result. The results can be used for the proof of global asymptotic stability by using continuously differentiable, positive definite functions which do not have a negative semi-definite derivative. Illustrating examples are provided.

Keywords: uniform robust global asymptotic stability; uniform robust global exponential stability; Lyapunov methods

Journal Article.  0 words. 

Subjects: Mathematics

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