Designing polynomial state feedback controllers to enlarge the domain of attraction in non-polynomial systems using a multidimensional gridding approach

This paper presents a technique of enlarging the domain of attraction (DOA) for non-polynomial systems using state feedback controllers. In order to deal with such a problem, we intend to extend our technique for the estimation of the DOA for non-polynomial systems presented in [1] to controller design, which maximizes the guaranteed DOA induced by quadratic Lyapunov functions (QLF). The state feedback controller design is formulated as a minimum-maximum optimization problem. A lower and upper bound of the approximation error of the non-polynomial terms on a predefined interval is determined. These bounds are used to adapt the theorem of Ehlich and Zeller [2] to non-polynomial systems. The aim of this contribution is to show that lower and upper bounds of the maximized DOA with a corresponding controller can be obtained. Moreover, two conditions for the tightness of the lower and upper bounds are established. The applicability of this method is demonstrated by an example with two different controllers.