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| Abstract: 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 consistent affine constraints on the coefficients. We show that there always exists an optimal polynomial with at most k − 1 inactive roots that is whose modulus is strictly less than the optimal root radius. We illustrate our results using some examples arising in feedback control. |
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