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Characterizing polynomials with roots in a semi-algebraic set

Jean B. Lasserre (lasserre***at***laas.fr)

Abstract: Consider a real polynomial $p$ and a semi-algebraic subset $S$ of the complex plane, defined by finitely many polynomial inequalities $g_k(z,\bar{z}) \geq 0$ for some complex polynomials $\{g_k\}$. We provide necessary and sufficient conditions on the coefficients of $p$ for the zeros of $p$ to be in $S$.

Keywords: algebraic geometry; root clustering

Category 1: Applications -- Science and Engineering (Control Applications )

Category 2: Other Topics (Other )

Citation: IEEE Trans. Automatic Control 49 (2004), pp. 727--730.

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Entry Submitted: 11/05/2003
Entry Accepted: 11/05/2003
Entry Last Modified: 10/05/2004

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