Robust Stabilization of Time-Delay Systems

  • Alexander Poznyak
  • Andrey Polyakov
  • Vadim Azhmyakov
Part of the Systems & Control: Foundations & Applications book series


In this chapter, we consider the class of uncertain time-delay affine-controlled systems in which a delay is admitted in state variables, and we show that the attractive ellipsoid method allows us to create a feedback that provides the convergence of any state trajectory of the controlled system from a given class to an ellipsoid whose “size” depends on the parameters of the applied feedback. Finally, we present a method for numerical calculation of these parameters that provides the “smallest” zone convergence for controlled trajectories.


Input time-delay Robust control Unknown delay 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexander Poznyak
    • 1
  • Andrey Polyakov
    • 2
  • Vadim Azhmyakov
    • 3
  1. 1.Automatic Control DepartmentCentro de Investigacion y Estudios AvanzadosMéxicoMexico
  2. 2.Non-AINRIA-LNEVilleneuve d’AscqFrance
  3. 3.Faculty of Electronic and Biomedical EngineeringUniversity of Antonio NariñoNeivaColombia

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