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Global stabilization in nonlinear discrete systems with time-delay

Author

Listed:
  • Anatoli Ivanov
  • Musa Mammadov
  • Sergei Trofimchuk

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. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Anatoli Ivanov & Musa Mammadov & Sergei Trofimchuk, 2013. "Global stabilization in nonlinear discrete systems with time-delay," Journal of Global Optimization, Springer, vol. 56(2), pages 251-263, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:251-263
    DOI: 10.1007/s10898-012-9862-y
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    References listed on IDEAS

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    1. Panos M. Pardalos & Vitaliy Yatsenko, 2008. "Control of Bilinear Systems," Springer Optimization and Its Applications, in: Optimization and Control of Bilinear Systems, chapter 0, pages 65-91, Springer.
    2. Panos M. Pardalos & Vitaliy Yatsenko, 2008. "Optimization and Control of Bilinear Systems," Springer Optimization and Its Applications, Springer, number 978-0-387-73669-3, June.
    3. John Creedy & Vance L. Martin (ed.), 1994. "Chaos and Non-Linear Models in Economics," Books, Edward Elgar Publishing, number 116.
    4. Musa A. Mamedov, 2009. "Asymptotical stability of optimal paths in nonconvex problems," Springer Optimization and Its Applications, in: Charles Pearce & Emma Hunt (ed.), Optimization, edition 1, chapter 0, pages 95-134, Springer.
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