An interval arithmetic approach for the estimation of the domain of attraction

Since the analysis of asymptotic stability is not sufficient for safety-critical nonlinear systems, the analysis of the domain of attraction is the focus of current research. While several approaches for polynomial systems were presented in the last years, based on sums of squares/linear matrix inequalities (SOS/LMIs) techniques or using a sampling method, only a few approaches are available for non-polynomial systems. In this paper we present a new branch-and-bound-method using the Lyapunov stability theory. It is based on interval arithmetic and delivers lower and upper bounds for the maximum contour line of a given Lyapunov function, which bounds a subset of the domain of attraction. Our approach can applied for polynomial systems as well as for non-polynomial systems.