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Asymptotics of solutions of difference equations with delays

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Abstract

We consider a linear scalar difference equation with several variable delays and constant coefficients. The coefficients and maximum admissible values of delays are supposed to be the set of parameters that define a family of equations of the investigated class. We obtain effective necessary and sufficient conditions of the uniform and exponential stability of solutions to all equations of the family, as well as the conditions of the sign-definiteness and monotonicity of stable solutions.

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Authors and Affiliations

  1. Perm National Research Polytechnic University, Komsomol’skii pr. 29, Perm, 614990, Russia

    V. V. Malygina & K. M. Chudinov

Authors
  1. V. V. Malygina
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  2. K. M. Chudinov
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Correspondence to V. V. Malygina.

Additional information

Original Russian Text © V.V. Malygina, K.M. Chudinov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 7, pp. 66–82.

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Malygina, V.V., Chudinov, K.M. Asymptotics of solutions of difference equations with delays. Russ Math. 60, 56–70 (2016). https://doi.org/10.3103/S1066369X16070082

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  • DOI: https://doi.org/10.3103/S1066369X16070082

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