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Exponential Stability of Autonomous Differential Equations of Neutral Type. I

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Abstract

In this paper the linear differential equations of neutral type are considered. The necessary and sufficient conditions are established under which the Cauchy function and the fundamental solution of these equations have exponential estimates. The results reduce the problem of exponential stability for autonomous equation of neutral type to two simpler ones: the problem about reversibility of the operator at the derivative and the problem about the location of zeros of the characteristic function on the complex plane, while it is not necessary to check the separation of zeros of the characteristic function from the imaginary axis.

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Funding

The work was supported by the state assignment of the Ministry of Science and Higher Education of the Russian Federation (project no. FSNM-2020-0028).

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  1. Perm National Research Polytechnic University, 614990, Perm, Russia

    A. S. Balandin

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  1. A. S. Balandin
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Correspondence to A. S. Balandin.

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Balandin, A.S. Exponential Stability of Autonomous Differential Equations of Neutral Type. I. Russ Math. 67, 9–22 (2023). https://doi.org/10.3103/S1066369X23030027

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  • DOI: https://doi.org/10.3103/S1066369X23030027

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