A. I. Dvirnyj, V. I. Slyn'ko, “Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations”, Mat. Zametki, 96:1 (2014), 22–35; Math. Notes, 96:1 (2014), 26

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Matematicheskie Zametki, 2014, Volume 96, Issue 1, Pages 22–35
DOI: https://doi.org/10.4213/mzm9021 (Mi mzm9021)

This article is cited in 14 scientific papers (total in 14 papers)

Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations

A. I. Dvirnyj^ab, V. I. Slyn'ko^ab

^a Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine
^b Hedmark University College, Norway

Full-text PDF (501 kB) Citations (14)

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DOI: https://doi.org/10.4213/mzm9021

Abstract: Classical theorems on the stability of the solutions of impulsive differential equations are further developed.

Keywords: impulsive differential equation, Lyapunov's direct method, Lyapunov (asymptotic) stability, Cauchy problem, equilibrium state stability, Hahn function class.

Received: 06.12.2010
Revised: 11.01.2013

English version:
Mathematical Notes, 2014, Volume 96, Issue 1, Pages 26–37
DOI: https://doi.org/10.1134/S0001434614070037

Bibliographic databases:

Document Type: Article

UDC: 517.929.21

Language: Russian

Citation: A. I. Dvirnyj, V. I. Slyn'ko, “Application of Lyapunov's Direct Method to the Study of the Stability of Solutions to Systems of Impulsive Differential Equations”, Mat. Zametki, 96:1 (2014), 22–35; Math. Notes, 96:1 (2014), 26–37

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Linking options:

https://www.mathnet.ru/eng/mzm9021

https://doi.org/10.4213/mzm9021

https://www.mathnet.ru/eng/mzm/v96/i1/p22

This publication is cited in the following 14 articles:

Sergey Dashkovskiy, Vitalii Slynko, 2023 European Control Conference (ECC), 2023, 1
Ivan Atamas, 2023 European Control Conference (ECC), 2023, 1
Dashkovskiy S., Slynko V., “Stability Conditions For Impulsive Dynamical Systems”, Math. Control Signal Syst., 34:1 (2022), 95–128
Slynko I V., Tunc C., Erdur S., “Sufficient Conditions of Interval Stability of a Class of Linear Impulsive Systems With a Delay”, J. Comput. Syst. Sci. Int., 59:1 (2020), 8–18
V. N. Kolesnichenko, V. I. Slyn'ko, “On the Dynamic Stability of Impulsive Mechanical Systems with Delay”, J Math Sci, 246:3 (2020), 337
V. I. Slyn'ko, O. Tunc, V. O. Bivziuk, “Application of commutator calculus to the study of linear impulsive systems”, Syst. Control Lett., 123 (2019), 160–165
S. V. Kravchuk, V. I. Slyn'ko, “Robust stability of linear periodic systems”, Autom. Remote Control, 80:12 (2019), 2108–2125
V. O. Bivziuk, V. I. Slyn'ko, “Sufficient conditions for the stability of linear periodic impulsive differential equations”, Sb. Math., 210:11 (2019), 1511–1530
V. Bivziuk, V. Slyn'ko, “Comparison principle for linear differential equations with periodic impulsive action”, 2019 57Th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Annual Allerton Conference on Communication Control and Computing, IEEE, 2019, 1023–1029
V. Slyn'ko, C. Tunc, “Stability of abstract linear switched impulsive differential equations”, Automatica, 107 (2019), 433–441
Vladyslav Bivziuk, Vitalii Slyn'ko, 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2019, 1023
V. I. Slyn'ko, C. Tunc, “Global asymptotic stability of nonlinear periodic impulsive equations”, Miskolc Math. Notes, 19:1 (2018), 595–610
V. I. Slyn'ko, “The stability conditions of linear periodic systems of ordinary differential equations”, St. Petersburg Math. J., 30:5 (2019), 885–900
V. I. Slyn'ko, C. Tunç, “Sufficient conditions for stability of periodic linear impulsive delay systems”, Autom. Remote Control, 79:11 (2018), 1989–2004

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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