Estimation of the domain of attraction for polynomial systems using multidimensional grids

Abstract

Investigation of the stability properties of stationary points of nonlinear systems lies at the heart of modern control engineering. In this contribution we show how the theorem of Ehlich and Zeller (1964) is used to compute subsets of the domain of attraction of asymptotically stable stationary points of polynomial systems. The theorem of Ehlich and Zeller is a tool to bound the values of a polynomial over an interval using the values of the polynomial on a finite grid in the interval. We present the generalizations of this theorem to multivariable polynomials and to trigonometric polynomials. A bisection strategy is presented which allows the guaranteed computation of a subset of the domain of attraction. An instructive example is presented and some conclusions and an outlook finish the contribution.