Explicit solutions for root optimization of a polynomial family

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a family of real or complex monic polynomials of fixed degree with one fixed affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or abscissa (largest real part of the roots). We give constructive methods for finding globally optimal solutions to these problems. In the real case, our methods are based on theorems that extend results in Raymond Chen's 1979 PhD thesis. In the complex case, our methods are based on theorems that are new, easier to state but harder to prove than in the real case. Examples are presented illustrating the results, including several fixed-order controller optimal design problems.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages485-488
Number of pages4
DOIs
StatePublished - 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

Explicit Solution
Polynomials
Roots
Controllers
Polynomial
Optimization
Abscissa
Complex Polynomials
Monic polynomial
Theorem
Controller Design
Modulus
Optimal Solution
Radius
Coefficient
Family
Optimal design

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Blondel, V. D., Gurbuzbalaban, M., Megretski, A., & Overton, M. L. (2010). Explicit solutions for root optimization of a polynomial family. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 485-488). [5718074] https://doi.org/10.1109/CDC.2010.5718074

Explicit solutions for root optimization of a polynomial family. / Blondel, Vincent D.; Gurbuzbalaban, Mert; Megretski, Alexander; Overton, Michael L.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 485-488 5718074.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Blondel, VD, Gurbuzbalaban, M, Megretski, A & Overton, ML 2010, Explicit solutions for root optimization of a polynomial family. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5718074, pp. 485-488, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5718074
Blondel VD, Gurbuzbalaban M, Megretski A, Overton ML. Explicit solutions for root optimization of a polynomial family. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 485-488. 5718074 https://doi.org/10.1109/CDC.2010.5718074
Blondel, Vincent D. ; Gurbuzbalaban, Mert ; Megretski, Alexander ; Overton, Michael L. / Explicit solutions for root optimization of a polynomial family. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 485-488
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