Geodesic
On the stability of solutions of nonlinear systems with impulse structure
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 624-636 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we review the results of the authors related to the study of the stability property of solutions for nonlinear systems of differential equations, on the right-hand side of which there are terms containing products of discontinuous functions and distributions. The solutions of such systems are formalized by the closure of the set of smooth solutions in the space of functions of bounded variation. For such systems, sufficient conditions are obtained for the asymptotic stability of unperturbed solutions.
Keywords: nonlinear systems, stability, asymptotic stability.
Mots-clés : impulse action 
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N. I. Zhelonkina; A. N. Sesekin. On the stability of solutions of nonlinear systems with impulse structure. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 624-636. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a4/

[1] A. M. Samoylenko, N. A. Perestyuk, Differential Equations with Impulse Action, Vishcha shkola Publ., Kiev, 1987, 288 pp. (In Russian)

[2] D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman, Harlow, 1993 | MR

[3] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989 | MR

[4] S. T. Zavalishchin, A. N. Sesekin, Dynamic Impulse Systems: Theory and Applications, Kluwer Academic Publ., Dordrecht, 1997, 268 pp. | MR

[5] A. N. Sesekin, “Dynamic systems with nonlinear impulse structure”, Proceedings of the Steklov Institute of Mathematics, 6:2 (2000), 497–514 (In Russian)

[6] B. M. Miller, E. Ya. Rubinovich, “Discontinuous solutions in the optimal control problems and their representation by singular spacetime transformations”, Automation and Remote Control, 2013, no. 12, 56–103 (In Russian)

[7] V. A. Dykhta, “Impulse Optimal Control in Economic and Quantum Electronics Models”, Automation and Remote Control, 1999, no. 11, 100–112 (In Russian) | MR

[8] V. A. Dykhta, O. N. Samsonyuk, Optimal Impulse Control with Applications, Fizmatlit Publ., Moscow, 2000, 256 pp. (In Russian) | MR

[9] D. L. Andrianov, V. O. Arbuzov, S. V. Ivliev, V. P. Maksimov, P. M. Simonov, “Dinamicheskie modeli ekonomiki: teoriya, prilozheniya, programmnaya realizatsiya”, Vestnik Permskogo universiteta. Seriya: Ekonomika, 2015, no. 4 (27), 8–32

[10] N. N. Krasovskiy, Motion Control Theory. Linear Systems, Nauka Publ., Moscow, 1968, 476 pp. (In Russian)

[11] V. Ya. Derr, “Ordinary ordinary differential equations with generalized functions in coefficients: a survey”, Functional and Differentional Equations: Theory and Applications, Proceedings of the conference dedicated to the 95th anniversary of the birth of prof. N. V. Azbeleva (Perm, 2017), Perm National Research Polytechnic University, Perm, 2017, 60–86 (In Russian)

[12] F. L. Pereira, G. N. Silva, “Lyapunov stability of measure driven impulsive systems”, Differential Equations, 40:8 (2004), 1059–1067 (In Russian) | MR

[13] D. Liberzon, A. Morse, “Basic problems in stability and and design of switched systems”, IEEE Control Syst. Mag., 19 (1999), 59–70 | DOI | MR

[14] A. N. Sesekin, N. I. Zhelonkina, “The stability of tubes of discontinuous solutions of dynamical systems”, AIP. Conference Proceeding, 1895 (2017), 050011 1–7 | DOI

[15] I. A. Kornilov, A. N. Sesekin, “On the stability of linear systems with a matrix containing generalized functions”, Bulletin of USTU-UPI, 2004, no. 3 (33), 386–388, Ekaterinburg (In Russian)

[16] N. I. Zhelonkina, A. N. Sesekin, “On Stability of Linear Systems with Impulsive Action at the Matrix”, Journal of Mathematical Sciences, 230:5 (2018), 673–676 (In Russian) | MR

[17] A. N. Sesekin, N. I. Zhelonkina, “Stability of nonlinear dynamical systems containing the product of discontinuous functions and distributions”, AIP. Conference Proceeding, 1789 (2016), 040010 1–8 | DOI