Robust Control of Switched Systems

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


This chapter deals with the problem of robust feedback design for a class of switched systems in the presence of bounded model uncertainties as well as external perturbations. Only the output of the system is supposed to be available for a designer. We consider nonlinear dynamic models under arbitrary switching mechanisms assuming that sample-switching times are known. Online state estimates are obtained by the use of a Luenberger-like observer using only current inputs and general information on the class of model uncertainties. The stabilization issue is solved in the sense of practical stability, and it is carried out by a linear (with respect to a current state estimate) feedback switching controller subject to an average dwell time scheme. We apply the newly elaborated (extended) version of the conventional attractive ellipsoid method for this purpose. Numerically implementable sufficient conditions for the practical stability of systems are derived using bilinear matrix inequalities. The effectiveness of the proposed method is illustrated by an example of a continuous stirred tank reactor in which only the temperature (not the concentration) is available during the process.


Switched systems Attractive ellipsoids Output-based control 


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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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