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 journalArticlepeer-review


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
Issue number12
StatePublished - 2012


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

ASJC Scopus subject areas

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


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