Nonlinear static state feedback controller design to enlarge the domain of attraction for a class of nonlinear systems

In this paper, the problem of computing state feedback controllers to enlarge the domain of attraction (DOA) in non-polynomial systems is considered. An optimization strategy based on a multidimensional gridding approach to estimate and to enlarge the guaranteed DOA of equilibrium points of non-polynomial systems is developed. Our intention is to extend our approach for the estimation of the DOA for non-polynomial systems presented in [1] to controller design, which maximizes the estimated DOA induced by a given quadratic Lyapunov function (QLF). An inner and an outer approximation of the enlarged DOA and the corresponding state feedback controller can be calculated. Two illustrative examples with different state feedback controllers demonstrate the effectiveness of the presented method.