Geodesic
Estimates of the exponential decay of solutions to linear systems of neutral type with periodic coefficients
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 3, pp. 96-103

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We consider the class of linear systems of delay differential equations with periodic coefficients. Using a special class of Lyapunov — Krasovskiĭ functionals, we establish conditions for the exponential stability of the zero solution and obtain estimates characterizing the exponential decay rate of solutions at infinity.
Keywords: time-delay system of neutral type, periodic coefficients, exponential stability, Lyapunov — Krasovskiĭ functional. 
I. I. Matveeva. Estimates of the exponential decay of solutions to linear systems of neutral type with periodic coefficients. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 3, pp. 96-103. http://geodesic.mathdoc.fr/item/SJIM_2019_22_3_a7/
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[1] L. E. Elsgolts, S. B. Norkin, Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971

[2] Dzh. Kheil, Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984

[3] D. G. Korenevskii, Ustoichivost dinamicheskikh sistem pri sluchainykh vozmuscheniyakh parametrov. Algebraicheskie kriterii, Naukova dumka, Kiev, 1989

[4] Izbrannye trudy N. V. Azbeleva, Izd-vo In-ta kompyuternykh issledovanii, M.–Izhevsk, 2012 | MR

[5] Yu. F. Dolgii, Ustoichivost periodicheskikh differentsialno-raznostnykh uravnenii, Izd-vo Ural. gos. un-ta, Ekaterinburg, 1996

[6] D. Ya. Khusainov, A. V. Shatyrko, Metod funktsii Lyapunova v issledovanii ustoichivosti differentsialno-funktsionalnykh sistem, Izd-vo Kiev. un-ta, Kiev, 1997 | MR

[7] V. B. Kolmanovskii, A. D. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Mathematics and its Applications, 463, Kluwer Acad. Publ., Dordrecht, 1999 | MR | Zbl

[8] W. Michiels, S. I. Niculescu, Stability, Control and Computation for Time-Delay Systems. An Eigenvalue-Based Approach, Advances in Design and Control, 27, Soc. Industrial and Appl. Math., Philadelphia, 2014 | MR

[9] R. P. Agarwal, L. Berezansky, E. Braverman, A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer Verl., N.Y., 2012 | MR | Zbl

[10] V. L. Kharitonov, Time-Delay Systems. Lyapunov Functionals and Matrices, Birkhauser, Basel, 2013 | MR | Zbl

[11] M. I. Gil', Stability of Neutral Functional Differential Equations, Atlantis Studies in Differential Equations, 3, Atlantis Press, Paris, 2014 | DOI | MR | Zbl

[12] A. S. Andreev, “Metod funktsionalov Lyapunova v zadache ob ustoichivosti funktsionalno-differentsialnykh uravnenii”, Avtomatika i telemekhanika, 2009, no. 9, 4–55 | Zbl

[13] E. Fridman, “Tutorial on Lyapunov-based methods for time-delay systems”, European J. Control, 20 (2014), 271–283 | DOI | MR | Zbl

[14] G. V. Demidenko, I. I. Matveeva, “Ustoichivost reshenii differentsialnykh uravnenii s zapazdyvayuschim argumentom i periodicheskimi koeffitsientami v lineinykh chlenakh”, Sib. mat. zhurn., 48:5 (2007), 1025–1040 | MR | Zbl

[15] I. I. Matveeva, “Otsenki reshenii odnogo klassa sistem nelineinykh differentsialnykh uravnenii s zapazdyvayuschim argumentom”, Sib. zhurn. industr. matematiki, 16:3 (2013), 122–132 | Zbl

[16] G. V. Demidenko, I. I. Matveeva, “Ob otsenkakh reshenii sistem differentsialnykh uravnenii neitralnogo tipa s periodicheskimi koeffitsientami”, Sib. mat. zhurn., 55:5 (2014), 1059–1077 | MR

[17] G. V. Demidenko, I. I. Matveeva, “Estimates for solutions to a class of time-delay systems of neutral type with periodic coefficients and several delays”, Electron. J. Qual. Theory Differ. Equ., 2015:83 (2015), 1–22 | DOI | MR

[18] I. I. Matveeva, “Ob eksponentsialnoi ustoichivosti reshenii periodicheskikh sistem neitralnogo tipa”, Sib. mat. zhurn., 58:2 (2017), 344–352 | MR | Zbl