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Spectral Test for Exponential Stability

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Abstract

Using the theory of commutative Banach algebras, we find an estimate of the solution of a higher-order linear differential equation; from this estimate, we derive a Lyapunov asymptotic stability test for this equation. Here the results by Faedo and Kharitonov on the Hurwitz conditions for families of polynomials find a natural application. Similar statements are obtained for a system of linear differential equations.

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Funding

The research of the first author was supported by the Russian Foundation for Basic Research under grant no. 19-01-00732.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, 394018, Russia

    I. D. Kostrub & A. I. Perov

Authors
  1. I. D. Kostrub
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  2. A. I. Perov
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Corresponding author

Correspondence to I. D. Kostrub.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 489–498 https://doi.org/10.4213/mzm13710.

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Kostrub, I.D., Perov, A.I. Spectral Test for Exponential Stability. Math Notes 113, 480–487 (2023). https://doi.org/10.1134/S0001434623030203

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  • DOI: https://doi.org/10.1134/S0001434623030203

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