Vincent D Blondel, Mert Gurbuzbalaban, Alexander Megretski, Michael L Overton
V. D. Blondel, M. Gurbuzbalaban, A. Megretski and M. L. Overton, "Explicit solutions for root optimization of a polynomial family," 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, 2010, pp. 485-488.
Publication year: 2010

The root radius of a polynomial is the maximum of the moduli of its roots (zeros). We
consider the following optimization problem: minimize 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. We show that there always exists an
optimal polynomial with at most k-1 k-1 inactive roots, that is, roots whose moduli are strictly
less than the optimal root radius. We illustrate our results using some examples arising in
feedback control.

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