Preview

Doklady of the National Academy of Sciences of Belarus

Advanced search

INVESTIGATION OF THE STABILITY OF GRADIENT SYSTEMS BY THE SECOND LYAPUNOV METHOD

https://doi.org/10.29235/1561-8323-2018-62-1-13-17

Abstract

In the article, new sufficient conditions of the extremum of the multivariable functions are shown. New sufficient tests of the stability and the asymptotic stability of gradient systems are stated. 

About the Author

Leonid B. Knyazhishche
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus

D. Sc. (Physics and Mathematics), Leading reseacher

11, Surganov Str., 220072, Minsk



References

1. Gaishun I. V., Knyazhishche L. B. Conditions for the stability of solutions of autonomous completely integrable equations. Differentsial’nye uravneniya = Differential equations, 1982, vol. 18, no. 8, pp. 1453–1456 (in Russian).

2. Gorokhovik V. V. Finite-dimensional optimization tasks. Minsk, Publishing Center of the Belarusian State University, 2007. 239 p. (in Russian).

3. Absil P. A., Kurdyka K. On the stable equilibrium points of gradient systems. Systems & Control Letters, 2006, vol. 55, no. 7, pp. 573–577. doi.org/10.1016/j.sysconle.2006.01.002

4. Rumyantsev V. V., Sosnitskii S. P. The stability of the equilibrium of holonomic conservative systems. Journal of Applied Mathematics and Mechanics, 1993. vol. 57, no. 6, pp. 1101–1122. doi.org/10.1016/0021-8928(93)90088-4


Review

Views: 872


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1561-8323 (Print)
ISSN 2524-2431 (Online)