On stability of solutions to neutral type systems
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 748-756.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of linear time-varying delay systems of neutral type with periodic coefficients. We obtain conditions for the exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity.
Keywords: time-varying delay systems, neutral type, periodic coefficients, exponential stability, estimates for solutions.
@article{SEMR_2019_16_a87,
     author = {I. I. Matveeva},
     title = {On stability of solutions to neutral type systems},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {748--756},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a87/}
}
TY  - JOUR
AU  - I. I. Matveeva
TI  - On stability of solutions to neutral type systems
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 748
EP  - 756
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a87/
LA  - ru
ID  - SEMR_2019_16_a87
ER  - 
%0 Journal Article
%A I. I. Matveeva
%T On stability of solutions to neutral type systems
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 748-756
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a87/
%G ru
%F SEMR_2019_16_a87
I. I. Matveeva. On stability of solutions to neutral type systems. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 748-756. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a87/

[1] L.E. El'sgol'ts, S.B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York–London, 1973 | MR | Zbl

[2] J.K. Hale, Theory of Functional Differential Equations, Applied Mathematical Sciences, 3, Springer–Verlag, New York–Heidelberg–Berlin, 1977 | DOI | MR | Zbl

[3] D.G. Korenevskii, Stability of Dynamical Systems under Random Perturbations of Parameters. Algebraic Criteria, Naukova Dumka, Kiev, 1989 (Russian) | MR

[4] N.V. Azbelev, V.P. Maksimov, L.F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations: Methods and Applications, Contemporary Mathematics and Its Applications, 3, Hindawi Publishing Corporation, Cairo, 2007 | MR | Zbl

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

[6] K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems, Control Engineering, Birkhäuser, Boston, 2003 | MR | Zbl

[7] R.P. Agarwal, L. Berezansky, E. Braverman, A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer, New York–Berlin, 2012 | MR | Zbl

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

[9] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Mathematics in Science and Engineering, 191, Academic Press, Boston, 1993 | MR | Zbl

[10] T. Erneux, Applied Delay Differential Equations, Surveys and Tutorials in the Applied Mathematical Sciences, 3, Springer, New York, 2009 | MR | Zbl

[11] G.V. Demidenko, I.I. Matveeva, “Stability of solutions to delay differential equations with periodic coefficients of linear terms”, Siberian Math. J., 48:5 (2007), 824–836 | DOI | MR | Zbl

[12] I.I. Matveeva, “Estimates of solutions to a class of systems of nonlinear delay differential equations”, J. Appl. Indust. Math., 7:4 (2013), 557–566 | DOI | MR | Zbl

[13] G.V. Demidenko, I.I. Matveeva, “On estimates of solutions to systems of differential equations of neutral type with periodic coefficients”, Siberian Math. J., 55:5 (2014), 866–881 | DOI | MR | Zbl

[14] 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 (2015), 83 | DOI | MR | Zbl

[15] I.I. Matveeva, “On exponential stability of solutions to periodic neutral-type systems”, Siberian Math. J., 58:2 (2017), 264–270 | DOI | MR | Zbl

[16] A.S. Andreev, “The method of Lyapunov functionals in the problem of the stability of functional-differential equations”, Autom. Remote Control, 70:9 (2009), 1438–1486 | DOI | MR | Zbl

[17] E. Fridman, “Tutorial on Lyapunov-based methods for time-delay systems”, European J. Control., 20:6 (2014), 271–283 | DOI | MR | Zbl

[18] V.L. Kharitonov, Time-Delay Systems. Lyapunov Functionals and Matrices, Control Engineering, Birkhauser/Springer, New York, 2013 | MR | Zbl

[19] D.Ya. Khusainov, A.T. Kozhametov, “Convergence of solutions of the neutral type nonautonomous systems”, Russian Math., 50:1 (2006), 65–69 | MR | Zbl

[20] A. Domoshnitsky, M. Gitman, R. Shklyar, “Stability and estimate of solution to uncertain neutral delay systems”, Boundary Value Problems, 2014 (2014), 55, 14 pp. | DOI | MR | Zbl

[21] S. Sh. Alaviani, “A necessary and sufficient condition for delay-independent stability of linear time-varying neutral delay systems”, J. Frankl. Inst., 351:5 (2014), 2574–2581 | DOI | MR | Zbl

[22] R.K. Romanovskii, L.V. Bel'gart, S.M. Dobrovol'skii, A.V. Rogozin, G.A. Trotsenko, Method of Lyapunov Functions for Almost Periodic Systems, Publishing House SB RAS, Novosibirsk, 2015

[23] G.V. Demidenko, I.I. Matveeva, “On stability of solutions to linear systems with periodic coefficients”, Siberian Math. J., 42:2 (2001), 282–296 | DOI | MR | Zbl

[24] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 2013 | MR | Zbl