IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i2p251-263.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9862-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9862-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. John Creedy & Vance L. Martin (ed.), 1994. "Chaos and Non-Linear Models in Economics," Books, Edward Elgar Publishing, number 116.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. P. Balasubramaniam & G. Nagamani, 2011. "Global Robust Passivity Analysis for Stochastic Interval Neural Networks with Interval Time-Varying Delays and Markovian Jumping Parameters," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 197-215, April.
    2. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.
    3. Vicente Costanza & Pablo S. Rivadeneira & Ruben D. Spies, 2011. "Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 26-46, April.
    4. Marcos Álvarez-Díaz & Alberto Álvarez, 2002. "Predicción No-Lineal De Tipos De Cambio: Algoritmos Genéticos, Redes Neuronales Y Fusión De Datos," Working Papers 0205, Universidade de Vigo, Departamento de Economía Aplicada.
    5. Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    6. Daniela Federici & Giancarlo Gandolfo, 2001. "Chaos and the exchange rate," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 11(2), pages 111-142.
    7. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    8. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    9. Marcos Álvarez-Díaz & Shawkat Hammoudeh & Rangan Gupta, 2013. "Detecting Predictable Non-linear Dynamics in Dow Jones Industrial Average and Dow Jones Islamic Market Indices using Nonparametric Regressions," Working Papers 201385, University of Pretoria, Department of Economics.
    10. Fernandez-Rodriguez, Fernando & Sosvilla-Rivero, Simon & Andrada-Felix, Julian, 1999. "Exchange-rate forecasts with simultaneous nearest-neighbour methods: evidence from the EMS," International Journal of Forecasting, Elsevier, vol. 15(4), pages 383-392, October.
    11. Foster, John, 1997. "The analytical foundations of evolutionary economics: From biological analogy to economic self-organization," Structural Change and Economic Dynamics, Elsevier, vol. 8(4), pages 427-451, October.
    12. Álvarez-Díaz, Marcos & Hammoudeh, Shawkat & Gupta, Rangan, 2014. "Detecting predictable non-linear dynamics in Dow Jones Islamic Market and Dow Jones Industrial Average indices using nonparametric regressions," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 22-35.
    13. Daniela Federici & Giancarlo Gandolfo, 2011. "The Euro/Dollar Exchange Rate: Chaotic or Non-Chaotic?," CESifo Working Paper Series 3420, CESifo.
    14. Marcos Álvarez-Díaz & Alberto Álvarez, 2003. "Predicción No-Lineal De Tipos De Cambio: Algoritmos Genéticos, Redes Neuronales Y Fusión De Datos," Working Papers 0301, Universidade de Vigo, Departamento de Economía Aplicada.
    15. Marjan Petreski, 2008. "To Fix Or To Float From Perspective Of Output Volatility And Vulnerability To Crisis," Journal Articles, Center For Economic Analyses, pages 9-24, June.
    16. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    17. Federici, Daniela & Gandolfo, Giancarlo, 2012. "The Euro/Dollar exchange rate: Chaotic or non-chaotic? A continuous time model with heterogeneous beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 670-681.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:251-263. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.