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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, Volume 28, Number 3, Pages 94–113
DOI: https://doi.org/10.21538/0134-4889-2022-28-3-94-113 (Mi timm1930) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Stability of Linear Time-Varying Differential Equations

V. A. Zaitsev, I. G. Kim

Udmurt State University, Izhevsk
Full-text PDF (278 kB) Citations (2)
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DOI: https://doi.org/10.21538/0134-4889-2022-28-3-94-113
Abstract: The article discusses the stability of linear differential equations with time-varying coefficients. It is shown that, in contrast to equations with time-invariant coefficients, the condition for the characteristic polynomial to be Hurwitz for a linear differential equation with time-varying coefficients is neither necessary nor sufficient for the asymptotic stability of the differential equation. It is proved that the analog of Kharitonov's theorem on robust stability does not hold if the coefficients of the differential equation are time-varying.
Keywords: linear differential equations, stability, time-varying system, stable polynomial, Kharitonov's theorem, robust stability.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-01265-22-00
This was supported by the Ministry of Science and Higher Education of the Russian Federation within project FEWS-2020-0010 (state contract no. 075-01265-22-00).
Received: 30.05.2022
Revised: 21.06.2022
Accepted: 04.07.2022
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2022, Volume 319, Issue 1, Pages S298–S317
DOI: https://doi.org/10.1134/S0081543822060268
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: 34A30, 34D20, 93D09
Language: Russian
Citation: V. A. Zaitsev, I. G. Kim, “On the Stability of Linear Time-Varying Differential Equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 3, 2022, 94–113; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S298–S317
Citation in format AMSBIB
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\paper On the Stability of Linear Time-Varying Differential Equations
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\issue 3
\pages 94--113
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages S298--S317
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