A robust and fast convergent interval analysis method for the calculation of internally controlled switching instants

Abstract

An interval analysis-based method for the root-finding of nonmonotonic polynomials is presented in this paper. It has been developed for numerical time-domain analysis of switched nonlinear networks, where internally controlled switching instants must be calculated as zeros of strongly nonmonotonic nonlinear functions. The method in based on an interval extension of Newton's operator resulting from the application of the mean-value theorem (m.v.t.) at the highest order to the polynomials whose zeros are sought. It is demonstrated that such interval extension is the most efficient one with respect to not only all those derived from the application of m.v.t. at any order lower than the maximum one but also to that one obtained with the centered form of the first derivative of the polynomial. A recursive algorithm for roots finding is presented which uses this optimal interval Newton's contraction mapping. Some examples drawn from switching converters time-domain analysis are proposed to outline the robustness and the sharp convergence of the method and its improvements with respect to other interval operators.