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A method for synthesis of robust interval polynomials using the extended root locus

The root locus method is proposed in the paper for calculating intervals of uncertainty for coefficients of the given (initial) polynomial with constant coefficients under perturbations, ensuring its robust stability regardless of whether the given polynomial is hurwitz or not. The method is based on introduction and application of the “extended root locus” notion and can be used for both, synthesis of interval robustly stable polynomials by setting up (adjusting) the unstable ones and analysis of the polynomial behavior under coefficient perturbations. Polynomial adjustment is performed by setting up each one of its coefficients separately and sequentially and determining values of coefficient variation intervals (intervals of uncertainty). The influence of each coefficient variation upon the polynomial roots dynamics (behavior) is considered and analyzed separately, and this influence could be observed in the root locus portraits. Root locus method is thus generalized to the cases when the number of polynomial variable coefficients is arbitrary.