 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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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 |
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