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IssuesArchive of Issues2010-4pp.384-388

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A.A. Zevin, "The necessary and sufficient conditions for the stability of linear systems with an arbitrary delay," J. Appl. Math. Mech. 74 (4), 384-388 (2010)
Year 2010 Volume 74 Issue 4 Pages 384-388
Title The necessary and sufficient conditions for the stability of linear systems with an arbitrary delay
Author(s) A.A. Zevin (Dnepropetrovsk, Ukarine, zevin@westa-inter.com)
Abstract A system of linear differential equations with a Hurwitz matrix A and a variable delay is considered. The system is assumed to be stable if it is stable for any delay function τ(t)≤h. The necessary and sufficient condition for stability, expressed using the eigenvalues of the matrix A and the quantity h, is found. It is established that the function τ(t), corresponding to the critical value of h, is constant or piecewise-linear depending on to which eigenvalue of matrix A (complex or real respectively) it corresponds. In the first case, the critical values of h in systems with a variable and constant delay are identical and, in the second case, they differ very slightly.
Received 24 March 2009
Link to Fulltext http://www.sciencedirect.com/science/journal/00218928
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