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      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.
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      • Bilkent Theses
      • Theses - Department of Electrical and Electronics Engineering
      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D.
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      Fixed order controller design via parametric methods

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      Author(s)
      Saadaoui, Karim
      Advisor
      Özgüler, A. Bülent
      Date
      2003
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      In this thesis, the problem of parameterizing stabilizing fixed-order controllers for linear time-invariant single-input single-output systems is studied. Using a generalization of the Hermite-Biehler theorem, a new algorithm is given for the determination of stabilizing gains for linear time-invariant systems. This algorithm requires a test of the sign pattern of a rational function at the real roots of a polynomial. By applying this constant gain stabilization algorithm to three subsidiary plants, the set of all stabilizing first-order controllers can be determined. The method given is applicable to both continuous and discrete time systems. It is also applicable to plants with interval type uncertainty. Generalization of this method to high-order controller is outlined. The problem of determining all stabilizing first-order controllers that places the poles of the closed-loop system in a desired stability region is then solved. The algorithm given relies on a generalization of the Hermite-Biehler theorem to polynomials with complex coefficients. Finally, the concept of local convex directions is studied. A necessary and sufficient condition for a polynomial to be a local convex direction of another Hurwitz stable polynomial is derived. The condition given constitutes a generalization of Rantzer’s phase growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polynomials.
      Keywords
      Hermite-Biehler theorem
      Local convex directions
      Regional pole placement
      Stabilization
      Stability
      First-order controllers
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      http://hdl.handle.net/11693/29422
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      • Dept. of Electrical and Electronics Engineering - Ph.D. / Sc.D. 167
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