Stability Analysis Methods

  • Germán A. RamosEmail author
  • Ramon Costa-Castelló
  • Josep M. Olm
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 446)


Repetitive control is a widely used strategy applied in the tracking/rejection of periodic signals, however, the performance of this controller can be seriously affected when the frequency of the reference/disturbance signal varies or is uncertain. One approach that overcomes this problem is the adaptation of the controller sampling period, nevertheless, the system framework changes from a Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. Indeed, the proposals applying this scheme in repetitive control do not provide formal stability proofs. This work presents two different methodologies aimed at analyse the system stability under these conditions. The first one uses a Linear Matrix Inequality gridding approach which provides necessary conditions for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies, entails a frequency variation interval for which the system stability can be assured.


Linear Time Invariant Repetitive Control Stability Analysis Method Repetitive Controller Uniform Exponential Stability 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Germán A. Ramos
    • 1
    Email author
  • Ramon Costa-Castelló
    • 2
  • Josep M. Olm
    • 3
  1. 1.Department of Electrical and Electronic EngineeringUniversidad Nacional de Colombia BogotáColombia
  2. 2.Escola Tècnica Superior d’Enginyeria Industrial de Barcelona (ETSEIB)Universitat Politècnica de Catalunya (UPC) BarcelonaSpain
  3. 3.Department of Applied Mathematics IV Universitat Politècnica de CatalunyaCastelldefelsSpain

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