Explicit solutions for root optimization of a polynomial family
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 globall...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73103 https://orcid.org/0000-0001-9088-0205 https://orcid.org/0000-0003-1563-800X |
| _version_ | 1826214978679472128 |
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| author | Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. |
| author_sort | Blondel, Vincent D. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T16:14:20Z |
| format | Article |
| id | mit-1721.1/73103 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:14:20Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/731032022-10-02T07:13:00Z Explicit solutions for root optimization of a polynomial family Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Blondel, Vincent D. Megretski, Alexandre 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. 2012-09-21T17:40:08Z 2012-09-21T17:40:08Z 2010-12 2010-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-4244-7745-6 0743-1546 http://hdl.handle.net/1721.1/73103 Blondel, Vincent D. et al. “Explicit Solutions for Root Optimization of a Polynomial Family.” Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 2010. 485–488. © Copyright 2010 IEEE https://orcid.org/0000-0001-9088-0205 https://orcid.org/0000-0003-1563-800X en_US http://dx.doi.org/10.1109/CDC.2010.5718074 Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 2010 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers (IEEE) IEEE |
| spellingShingle | Blondel, Vincent D. Gurbuzbalaban, Mert Megretski, Alexandre Overton, Michael L. Explicit solutions for root optimization of a polynomial family |
| title | Explicit solutions for root optimization of a polynomial family |
| title_full | Explicit solutions for root optimization of a polynomial family |
| title_fullStr | Explicit solutions for root optimization of a polynomial family |
| title_full_unstemmed | Explicit solutions for root optimization of a polynomial family |
| title_short | Explicit solutions for root optimization of a polynomial family |
| title_sort | explicit solutions for root optimization of a polynomial family |
| url | http://hdl.handle.net/1721.1/73103 https://orcid.org/0000-0001-9088-0205 https://orcid.org/0000-0003-1563-800X |
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