Explicit solutions for root optimization of a polynomial family with one affine constraint

Vincent D. Blondel, Mert Gurbuzbalaban, Alexandre Megretski, Michael L. Overton

Research output: Contribution to journalArticle

Abstract

Given a family of real or complex monic polynomials of fixed degree with one affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or root abscissa (largest real part of the roots). We give constructive methods for efficiently computing the globally optimal value as well as an optimal polynomial when the optimal value is attained and an approximation when it is not. An optimal polynomial can always be chosen to have at most two distinct roots in the real case and just one distinct root in the complex case. Examples are presented illustrating the results, including several fixed-order controller optimal design problems.

Original languageEnglish (US)
Article number6209388
Pages (from-to)3078-3089
Number of pages12
JournalIEEE Transactions on Automatic Control
Volume57
Issue number12
DOIs
StatePublished - 2012

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Polynomials
Controllers
Optimal design

Keywords

  • Control system synthesis
  • optimization
  • output feedback
  • polynomials
  • stability

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

Cite this

Explicit solutions for root optimization of a polynomial family with one affine constraint. / Blondel, Vincent D.; Gurbuzbalaban, Mert; Megretski, Alexandre; Overton, Michael L.

In: IEEE Transactions on Automatic Control, Vol. 57, No. 12, 6209388, 2012, p. 3078-3089.

Research output: Contribution to journalArticle

Blondel, Vincent D. ; Gurbuzbalaban, Mert ; Megretski, Alexandre ; Overton, Michael L. / Explicit solutions for root optimization of a polynomial family with one affine constraint. In: IEEE Transactions on Automatic Control. 2012 ; Vol. 57, No. 12. pp. 3078-3089.
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