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Global stabilization in nonlinear discrete systems with time-delay

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Abstract

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, P.O. Box PSU, Lehman, PA, 18627, USA

    Anatoli F. Ivanov

  2. University of Ballarat, Ballarat, VIC, 3353, Australia

    Musa A. Mammadov

  3. National ICT Australia, VRL, Melbourne, VIC, 3010, Australia

    Musa A. Mammadov

  4. Instituto de Matematica y Fisica, Universidad de Talca, Casilla 747, Talca, Chile

    Sergei I. Trofimchuk

Authors
  1. Anatoli F. Ivanov
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  2. Musa A. Mammadov
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  3. Sergei I. Trofimchuk
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Corresponding author

Correspondence to Musa A. Mammadov.

Additional information

Anatoli Ivanov was supported in part by CONICYT (Chile), project MEC 801100006. S. Trofimchuk was partially supported by FONDECYT (Chile), project 1110309.

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Ivanov, A.F., Mammadov, M.A. & Trofimchuk, S.I. Global stabilization in nonlinear discrete systems with time-delay. J Glob Optim 56, 251–263 (2013). https://doi.org/10.1007/s10898-012-9862-y

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  • DOI: https://doi.org/10.1007/s10898-012-9862-y

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