Explicit solutions for root optimization of a polynomial family

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

doi:10.1109/CDC.2010.5718074

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 proceeding › Conference 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 language	English (US)
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	485-488
Number of pages	4
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5718074
State	Published - 2010
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: Dec 15 2010 → Dec 17 2010

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	12/15/10 → 12/17/10

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2010.5718074

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). Article 5718074 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2010.5718074

Explicit solutions for root optimization of a polynomial family. / Blondel, Vincent D.; Gurbuzbalaban, Mert; Megretski, Alexander et al.
2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 485-488 5718074 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference 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, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 485-488, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5718074

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title = "Explicit solutions for root optimization of a polynomial family",

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.",

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language = "English (US)",

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series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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AU - Megretski, Alexander

AU - Overton, Michael L.

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Y1 - 2010

N2 - 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.

AB - 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.

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BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

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Explicit solutions for root optimization of a polynomial family

Abstract

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