Journal Article

Stability and hyperbolicity of linear systems with delayed state: a matrix-pencil approach

SILVIU-IULIAN NICULESCU

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 15, issue 4, pages 331-347
Published in print December 1998 | ISSN: 0265-0754
Published online December 1998 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/15.4.331
Stability and hyperbolicity of linear systems with delayed state: a matrix-pencil approach

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This note focuses on the problem of asymptotic stability and hyperbolicity of a class of linear systems described by delay-differential equations including commensurable delays. An unitary approach for the considered problems is proposed via a matrix-pencil technique. Necessary and sufficient conditions, delay-independent or delay-dependent, are given in terms of the generalized eigenvalue distribution of two constant and regular matrix pencils: one associated with finite time delays and the other one associated with infinite delay. Furthermore, the proposed results are easy to check in numerical examples. An example from the neural-network field has also been considered.

Keywords: delay systems; asymptotic stability; hyperbolicity; matrix pencil; dichotomy

Journal Article.  0 words. 

Subjects: Mathematics

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