Robust Performance Analysis of Discrete-Time Periodic Systems

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


Chapter  7 is dedicated to the analysis of discrete-time periodic systems by means of SV-LMIs. For that special case the SV-LMIs have interesting non-causal system interpretations. Similarly to the LTI case, SV-LMIs are effective for reducing the conservatism of the analysis results when dealing with discrete-time periodic systems affected by polytopic uncertainties.


Discrete-time Periodic Systems Robust Stability Analysis Polytopic Uncertainties Schur Stability Conservative Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bittanti S, Colaneri P (1996) Analysis of discrete-time linear periodic systems. In: Leondes CT (ed) Control and dynamic systems. Academic Press, New York, pp 313–339Google Scholar
  2. 2.
    Bittanti S, Bolzern P, Colaneri P (1985) The extended periodic Lyapunov lemma. Automatica 21:603–605MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    De Souza CE, Trofino A (2000) An LMI approach to stabilization of linear discrete-time periodic systems. Int J Control 73:696–709CrossRefzbMATHGoogle Scholar
  4. 4.
    Ebihara Y, Peaucelle D, Arzelier D (2010) Analysis of uncertain discrete-time linear periodic systems based on system lifting and LMIs. Eur J Control 16(5):532–544MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bittanti S, Colaneri P (2009) Periodic systems: filtering and control. Springer, LondonGoogle Scholar
  6. 6.
    Zhang C, Zhang J, Furuta K (1997) Analysis of \(H_2\) and \(H_\infty \) performance of discrete periodically time-varying controllers. Automatica 33(4):619–634MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    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
  8. 8.
    Ebihara Y, Peaucelle D, Arzelier D (2008) Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. In: Proceedings of the conference on decision and control, pp 5438–5443Google Scholar
  9. 9.
    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
  10. 10.
    Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim Methods Softw 11–12:625–653MathSciNetCrossRefGoogle Scholar
  11. 11.
    Löfberg J (2004) YALMIP: a toolbox for modeling and optimization in MATLAB. In: Proceedings of the IEEE computer aided control system design, pp 284–289Google 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

Personalised recommendations