V.A. Zaitsev, I.G. Kim. On the stability of linear time-varying differential equations ... P. 94-113

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 May 30, 2022

Revised June 21, 2022

Accepted July 4, 2022

Funding Agency: 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).

Vasilii Aleksandrovich Zaitsev, Dr. Phys.-Math. Sci., Udmurt State University, Izhevsk, 426034 Russia, e-mail: verba@udm.ru

Inna Geral’dovna Kim, Udmurt State University, Izhevsk, 426034 Russia, e-mail: kimingeral@gmail.com


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Cite this article as: V.A. Zaitsev, I.G. Kim. On the stability of linear time-varying differential equations. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 3, pp. 94–113; Proceedings of the Steklov Institute of Mathematics (Suppl.), 2022, Vol. 319, Suppl. 1, pp. S298–S317.