Robust Controller Synthesis of Periodic Discrete-Time Systems

  • Yoshio EbiharaEmail author
  • Dimitri Peaucelle
  • Denis Arzelier
Part of the Communications and Control Engineering book series (CCE)


Finally, Chapter 8 deals with state-feedback controller synthesis for discrete-time periodic systems. By introducing S-variables and applying change of variables that is almost identical to the LTI case, we can readily obtain SV-LMIs for periodic state-feedback controller synthesis. We illustrate by numerical examples that the SV-LMIs are indeed effective in conservatism reduction when dealing with discrete-time periodic systems affected by polytopic uncertainties.


  1. 1.
    Bittanti S, Colaneri P (2009) Periodic systems: filtering and control. Springer, LondonGoogle Scholar
  2. 2.
    Farges C, Peaucelle D, Arzelier D, Daafouz J (2007) Robust H\(_2\) performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Syst Control Lett 56:159–166MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ebihara Y, Peaucelle D, Arzelier D (2011) Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems. Automatica 47(1):14–25MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ebihara Y (2013) Periodically time-varying memory state-feedback for robust H\(_2\) control of uncertain discrete-time linear systems. Asian J Control 15(2):409–419MathSciNetCrossRefGoogle Scholar
  5. 5.
    Trégouët JF, Peaucelle D, Arzelier D, Ebihara Y (2013) Periodic memory state-feedback controller: new formulation, analysis and design results. IEEE Trans Autom Control 58(8):1986–2000CrossRefGoogle Scholar
  6. 6.
    Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim Meth Softw 11–12:625–653MathSciNetCrossRefGoogle Scholar
  7. 7.
    Löfberg J (2004) YALMIP: a toolbox for modeling and optimization in MATLAB. In: Proceedings IEEE Computer Aided Control System Design, pp 284–289, 2004Google Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Yoshio Ebihara
    • 1
    Email author
  • Dimitri Peaucelle
    • 2
  • Denis Arzelier
    • 2
  1. 1.Department of Electrical EngineeringKyoto UniversityKyotoJapan
  2. 2.Laboratory for Analysis and Architecture of Systems ScienceNational Centre for Scientific ResearchToulouseFrance

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