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      Stable controllers for robust stabilization of systems with infinitely many unstable poles

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      Author
      Wakaiki, M.
      Yamamoto, Y.
      Özbay, Hitay
      Date
      2013
      Source Title
      Systems and Control Letters
      Print ISSN
      0167-6911
      Publisher
      Elsevier
      Volume
      62
      Issue
      6
      Pages
      511 - 516
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation-minimization by a unit element. Next, by the modified Nevanlinna-Pick interpolation, we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller. In addition, we find stable controllers to provide robust stability. We also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system.
      Keywords
      H∞ control
      Infinite dimensional systems
      Robust stabilization
      Strong stabilization
      Infinite-dimensional system
      Linear time-invariant
      Lower and upper bounds
      Nevanlinna-Pick interpolation
      Repetitive control system
      Robust stabilization
      Single input single output
      Strong stabilization
      Control system analysis
      Interpolation
      Poles
      Robustness (control systems)
      Stabilization
      Permalink
      http://hdl.handle.net/11693/20996
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.sysconle.2013.02.005
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      • Department of Electrical and Electronics Engineering 3524
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