Stability conditions of linear time-varying dynamical systems
- 1 Dr.Sc.(Phys.-Math.), Professor, Main Research Scientist, FRC «Computer Science and Control» of RAS (Moscow); Main Research Scientist, V.A. Trapeznikov Institute of Control Sciences of RAS (Moscow)
- 2 Ph.D.(Phys.-Math.), Associate Professor, Kaluga branch of the Bauman MSTU
Keywords:
stabilitylinear nonstationary systemLyapunov functioncoefficient conditionslogarithmic norm of a matrix
Abstract
Qualitative properties of solutions of nonstationary linear systems of differential equations with continuous coefficients are studied. Stability conditions are obtained on the basis of the Lyapunov function method and the conditions of diagonal domination. The properties of the logarithmic measure of the matrix of the right-hand side of the system are used for stability analysis.
How to cite
Дружинина О.В., Лисовский Е.В. Условия устойчивости нестационарных линейных динамических систем // Электромагнитные волны и электронные системы. 2018. № 4. С. 55–60.
References
- Mixajlov F.A., Teryaev E.D., Bulekov V.P., Dankov G.Yu., Salikov L.M., Stepan’yancz G.A. Dinamika nestaczionarny’x linejny’x sistem. M.: Nauka. 1967.
- Mixajlov F.A. Analiz i sintez nestaczionarny’x linejny’x sistem. M.: Mashinostroenie. 1977.
- Starzhinskij V.M. Prikladny’e metody’ nelinejny’x kolebanij. M.: Nauka. 1977.
- Xartman F. Oby’knovenny’e differenczial’ny’e uravneniya. M.: Mir. 1970.
- Gajshun I.V. Vvedenie v teoriyu linejny’x nestaczionarny’x sistem. Minsk: Izd-vo In-ta matematiki NAN Belarusi. 1999.
- Makarov E.K., Popova S.N. Upravlyaemost’ asimptoticheskix invariantov nestaczionarny’x linejny’x sistem. Minsk: Belarus. navuka. 2012.
- Kalenova V.I., Morozov V.M. Linejny’e nestaczionarny’e sistemy’ i ix prilozheniya k zadacham mexaniki. M.: Fizmatlit. 2010.
- Chetaev N.G. Ustojchivost’ dvizheniya. M.: Nauka. 1992.
- Zubov V.I. Ustojchivost’ dvizheniya. M.: Vy’sshaya shkola. 1973.
- Persidskij K.P. Izbranny’e trudy’. Alma-Ata: Nauka. T. 2.
- Shestakov A.A. Obobshhenny’j pryamoj metod Lyapunova dlya sistem s raspredelenny’mi parametrami. M.: Nauka. 1990 (Izd. 2-e, dopoln. M.: URSS. 2007).
- Coppel W.A. Stability and Asymptotic Behavior of Differential Equations. Heath and Co. Math. Monograph. Boston. 1965.
- Bojkov I.V. Ustojchivost’ reshenij differenczial’ny’x uravnenij. Penza: Izdatel’stvo Penzenskogo gosudarstvennogo universiteta. 2008.
- Druzhinina O.V. Koe’fficzientny’e priznaki asimptoticheskoj ustojchivosti sostoyaniya ravnovesiya mexanicheskix sistem, modeliruemy’x nestaczionarny’mi linejny’mi differenczial’ny’mi uravneniyami v banaxovom prostranstve // Dep. v VINITI (№ 476-V94). 55 s.
- Druzhinina O.V. Priznaki asimptoticheskoj prochnosti i neprochnosti dvizheniya dinamicheskoj sistemy’ // DAN. 1997. T. 355. № 4. S. 476−478.
- Druzhinina O.V., Lisovskij E.V. Usloviya ustojchivosti nestaczionarny’x sistem differenczial’ny’x uravnenij // Nelinejny’j mir. 2017. T. 15. № 3. S. 54−58.