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One Version of the Theorem on Stability by the First Approximation in the Discrete-Time Case

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Abstract

We extend an analog of the Chetaev–Malkin–Massera theorem on stability by the first approximation for differential systems to discrete-time systems in which the linear first approximation system is subjected to linear and nonlinear perturbations. The result is stated in terms of the characteristic exponents and the Lyapunov irregularity coefficient of the linear first approximation system.

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REFERENCES

  1. Demidovich, V.B., On a stability test for difference equations, Differ. Uravn., 1969, vol. 5, no. 7, pp. 1247–1255.

    Google Scholar 

  2. Kuznetsov, N.V. and Leonov, G.A., Stability of discrete-time systems by the first approximation, Vestn. S.-Peterb. Univ. Ser. 1 , 2003, no. 1, pp. 28–35.

  3. Kuznetsov, N.V. and Leonov, G.A., Criteria for stability of nonlinear discrete-time systems by the first approximation, Vestn. S.-Peterb. Univ.. Ser. 1., 2005, no. 2, pp. 55–63.

  4. Lyapunov, A.M., Obshchaya zadacha ob ustoichivosti dvizheniya (General Problem of Stability of Motion), Moscow–Leningrad: GITTL, 1950.

    Google Scholar 

  5. Bylov, B.F., Vinograd, R.E., Grobman, D.M., and Nemytskii, V.V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti (Theory of Lyapunov Exponents and Its Applications to Stability Problems), Moscow: Nauka, 1966.

    Google Scholar 

  6. Kuznetsov, N.V., Stability of discrete-time systems, Extended Abstract of Cand. Sci. (Phys.-Math.) Dissertation, St. Petersburg, 2004.

  7. Leonov, G.A., Khaoticheskaya dinamika i klassicheskaya teoriya ustoichivosti dvizheniya (Chaotic Dynamics and Classical Theory of Stability of Motion), Moscow–Izhevsk: R & C Dynamics, 2006.

    Google Scholar 

  8. Adrianova, L.Ya., Vvedenie v teoriyu lineinykh sistem differentsial’nykh uravnenii (Introduction to the Theory of Linear Systems of Differential Equations), St. Petersburg: Izd. S.-Peterb. Univ., 1992.

    Google Scholar 

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Authors and Affiliations

  1. Yaroslav-the-Wise Novgorod State University, Novgorod, 173003, Russia

    A. V. Lasunsky

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  1. A. V. Lasunsky
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Correspondence to A. V. Lasunsky.

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Translated by V. Potapchouck

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Lasunsky, A.V. One Version of the Theorem on Stability by the First Approximation in the Discrete-Time Case. Diff Equat 57, 408–413 (2021). https://doi.org/10.1134/S0012266121030125

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  • DOI: https://doi.org/10.1134/S0012266121030125

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