The Kharitonov theorem and its applications in symbolic mathematical computation †

The Kharitonov theorem provides a means of performing sensitivity analysis for the complex roots of polynomials whose coefficients (in power base) are perturbed. In particular, it gives a computationally feasible algorithm for testing if the roots remain contained on the left hand side of the Gaussian plane if one perturbes each coefficient of a monic polynomial by a given amount. We survey an abstract approach that leads to generalizations from the literature and our own, which imposes containment of the roots within a circular sector centered in the origin of the Gaussian plane. 1