Journal Article

On stability conditions for systems with periodic state-dependent coefficients: a counter example

Shah Muhammad and Jacob van der Woude

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 28, issue 1, pages 97-102
Published in print March 2011 | ISSN: 0265-0754
Published online December 2010 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnq027
On stability conditions for systems with periodic state-dependent coefficients: a counter example

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In this paper, we consider non-linear systems in state-dependent coefficient form, i.e. non-linear systems expressed in a linear structure with state-dependent coefficient matrices. In a previous paper, we showed by means of a counter example that conditions existing in literature, which were claimed to be sufficient for global asymptotic stability, in fact are not sufficient. In this paper, we show that for pseudo-linear systems with coefficient matrices that depend on the state in a periodic way, the referred existing conditions remain insufficient. Hence, the addition of the requirement that the state dependency of the coefficient matrices is periodic, does not contribute in achieving global asymptotic stability.

Keywords: non-linear systems; state-dependent coefficient form; global asymptotic stability; periodic state dependency

Journal Article.  0 words. 

Subjects: Mathematics

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