Newton algorithms via control Liapunov functions for polynomial zero finding

The Newton-Raphson method is approached from a control perspective, leading to variants of this classical algorithm. One variant, a "variable structure" Newton-like algorithm, is shown to provide a rigorous justification for the nonsmooth Kokotovic-Siljak zero finding method for polynomials with complex coefficients and also leads to extensions in which knowledge of bounds on the zeros can be incorporated into the algorithm.