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

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 comp...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2012-12, Vol.57 (12), p.3078-3089
Main Authors: Blondel, V. D., Gurbuzbalaban, M., Megretski, A., Overton, M. L.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Approximation methods
Automatic control
Computation
Computer science
control theory
systems
Construction
Control system synthesis
Control theory. Systems
Exact sciences and technology
Mathematical analysis
Mathematical models
Optimization
Output feedback
Polynomials
Roots
Stability
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2202069