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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
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.
Received: 30.05.2022 Revised: 21.06.2022 Accepted: 04.07.2022
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
Linking options:
https://www.mathnet.ru/eng/timm1930 https://www.mathnet.ru/eng/timm/v28/i3/p94
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Abstract page: | 113 | Full-text PDF : | 35 | References: | 21 | First page: | 6 |
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