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Analysis of Peak Effects in the Solutions of a Class of Difference Equations

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Abstract

We consider a class of well-known high-order trinomial linear difference equations and analyze the non-asymptotic behavior of their solutions under non-zero initial conditions from the unit box. It is shown that, for certain subsets of coefficients in the stability domain, there always exist initial conditions leading to peak, a large deviation of solutions from the equilibrium position, and that these deviations may take arbitrarily large values. Various special cases are studied, numerical examples are presented.

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ACKNOWLEDGMENTS

The author is grateful to V.N. Chestnov and D.V. Shatov for their valuable instructions for improving the quality of the presentation of the material.

Funding

The results of Sections 3.2.2–3.2.6 were obtained within the Russian Science Foundation grant (project no. 21-71-30005), https://rscf.ru/en/project/21-71-30005/.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    P. S. Shcherbakov

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    P. S. Shcherbakov

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  1. P. S. Shcherbakov
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Correspondence to P. S. Shcherbakov.

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This paper was recommended for publication by M.V. Khlebnikov, a member of the Editorial Board

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Shcherbakov, P.S. Analysis of Peak Effects in the Solutions of a Class of Difference Equations. Autom Remote Control 85, 512–521 (2024). https://doi.org/10.1134/S0005117924060092

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