An interval arithmetic approach for the estimation of the robust domain of attraction for nonlinear autonomous systems with nonlinear uncertainties

Abstract

This paper investigates an algorithm for the estimation of the robust domain of attraction (RDA) for nonlinear autonomous systems with uncertain parameters. Usually, an exact mathematical model for a system is assumed. In real systems, there are uncertainties caused by e. g. temperature drift or friction, which increases while lifetime. Furthermore, system parameters could be varied by the user. However, time-dependent parameters fluctuate in an known interval. Therefore, it is important to determine the domain of attraction for all configurations of the system. The presented method can estimate the RDA for systems with linear as well as nonlinear uncertainties. In this algorithm, interval arithmetic is used to determine successively the RDA by an inner and an outer bound. As a result, the algorithm delivers an enclosure of the Lyapunov function (LF) contour line c*.