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Asymptotic Stability of Solutions to Perturbed Linear Difference Equations with Periodic Coefficients

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Abstract

We consider perturbed linear systems of difference equations with periodic coefficients. The zero solution of a nonperturbed system is assumed asymptotically stable, i.e., all eigenvalues of the monodromy matrix belong to the unit disk {|λ|<1}. We obtain conditions on the perturbation of this system under which the zero solution of the system is asymptotically stable and also establish continuous dependence of one class of numeric characteristics of asymptotic stability of solutions on the coefficients of the system.

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Authors and Affiliations

  1. Research Center of Applied Mathematics, Selcuk University, Konya, Turkey

    K. Aydin & H. Bulgak

  2. Sobolev Institute of Mathematics, Novosibirsk

    G. V. Demidenko

Authors
  1. K. Aydin
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  2. H. Bulgak
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  3. G. V. Demidenko
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Aydin, K., Bulgak, H. & Demidenko, G.V. Asymptotic Stability of Solutions to Perturbed Linear Difference Equations with Periodic Coefficients. Siberian Mathematical Journal 43, 389–401 (2002). https://doi.org/10.1023/A:1015492015263

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  • DOI: https://doi.org/10.1023/A:1015492015263

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