Explicit solutions for root optimization of a polynomial family
Author(s)Blondel, Vincent D.; Gurbuzbalaban, Mert; Megretski, Alexandre; Overton, Michael L.
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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.
DepartmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systems
Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 2010
Institute of Electrical and Electronics Engineers (IEEE)
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
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