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.
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).
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
\Bibitem{ZaiKim22}
\by V.~A.~Zaitsev, I.~G.~Kim
\paper On the Stability of Linear Time-Varying Differential Equations
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2022
\vol 28
\issue 3
\pages 94--113
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\crossref{https://doi.org/10.21538/0134-4889-2022-28-3-94-113}
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2022
\vol 319
\issue , suppl. 1
\pages S298--S317
\crossref{https://doi.org/10.1134/S0081543822060268}
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Linking options:
https://www.mathnet.ru/eng/timm1930
https://www.mathnet.ru/eng/timm/v28/i3/p94
This publication is cited in the following 2 articles:
M. Hammami, R. Hamlili, V. A. Zaitsev, “On the stability in variation of non-autonomous differential equations with perturbations”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:2 (2024), 222–247
Vasilii Zaitsev, “On the asymptotic stability of linear difference equations with time-varying coefficients”, MATH, 8:10 (2023), 23734
Citation in format AMSBIB
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