Semi-global enlargement of domain of attraction for a class of affine nonlinear systems

In this paper, a new approach to enlarge the domain of attraction of a nonlinear affine system based on Zubov Theorem is suggested. The affine systems which are studied in this paper some times have some constraints that coping with them are difficult. The proposed approach may alleviate these difficulties by introducing an extended controller design methodology. The controller can extend the domain of attraction as an n-dimensional ellipsoid in a way that the diameters of ellipsoid, may be used as the tuning factors for shaping and enlarging it as much as possible. In this approach, the ratios of diameters are not crucial. In other words, it is possible to stretch the domain of attraction along some directions and compress it along the others. The simulation results on the Van der Pole system and two case studies, namely, a vehicle dynamics and an inverted pendulum show the efficiency of the method.