Explicit Solutions for Root Optimization of a Polynomial Family with One Affine Constraint

Blondel, Vincent;Gurbuzbalaban, Mert;Megretski, Alexandre;Overton, Michael L.
(2012) IEEE Transactions on Automatic Control — Vol. 57, n° 12, p. 3078-3089 (2012)

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Authors
  • Blondel, Vincentorcid-logoUCLouvain
    Author
  • Gurbuzbalaban, MertNew York University
    Author
  • Megretski, AlexandreMIT
    Author
  • Overton, Michael L.New York University
    Author
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.
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Blondel, V., Gurbuzbalaban, M., Megretski, A., & Overton, M. L. (2012). Explicit Solutions for Root Optimization of a Polynomial Family with One Affine Constraint. IEEE Transactions on Automatic Control, 57(12), 3078-3089. https://doi.org/10.1109/TAC.2012.2202069 (Original work published 2012)