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The necessary and sufficient conditions for the stability of linear systems with an arbitrary delay

✍ Scribed by A.A. Zevin

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
220 KB
Volume
74
Category
Article
ISSN
0021-8928

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✦ Synopsis

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 (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 (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.

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