 | | 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.M. Kovalev, "Invariance and asymptotic stability," J. Appl. Math. Mech. 75 (3), 317-322 (2011) |
| Year |
2011 |
Volume |
75 |
Issue |
3 |
Pages |
317-322 |
| Title |
Invariance and asymptotic stability |
| Author(s) |
A.M. Kovalev (Donetsk, Ukraine, kovalev@iamm.ac.donetsk.ua) |
| Abstract |
The stability of the zero solution of an autonomous non-linear system is considered. The problem of finding the variables in relation to which the solution is asymptotically stable if the Lyapunov function with a sign-definite derivative is known, is formulated and solved. The maximality of the set in relation to which the solution is asymptotically stable is established. The investigation is based on the method of auxiliary functions and clarifies the relation between the properties of invariance and the asymptotic stability of dynamical systems. The constructiveness of the results obtained is demonstrated by an example. |
| Received |
16 October 2010 |
| Link to Fulltext |
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