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Polynomial root radius optimization with affine constraints. (English) Zbl 1377.26015

The problem of minimizing the root radius over monic polynomials of degree \(n\) with either real or complex coefficients, subject to \(k\) linearly independent affine constraints on the coefficients is investigated. The main result states that there always exists an optimal polynomial with at most \(k-1\) roots whose moduli are strictly less than the optimal root radius, so-called inactive roots and its (quite involved) proof is divided into several steps, some of which interesting also per se. Illustrative examples arising in feedback control and some interesting ideas for future work complete the paper.

MSC:

26C10 Real polynomials: location of zeros
49J52 Nonsmooth analysis

Software:

Matlab
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Full Text: DOI Link

References:

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