State feedback controller design to enlarge the domain of attraction in polynomial systems

In this paper, a technique of enlarging the domain of attraction (DOA) for polynomial systems using state feedback controllers is considered. In order to deal with such a problem, we present a technique for computing state feedback controllers, which maximize the guaranteed DOA induced by a quadratic Lyapunov function (QLF). The state feedback controller design is formulated as a minimum-maximum optimization problem. The main theme of this contribution is to show that lower and upper bounds of the maximized DOA and a corresponding controller can be calculated. Moreover, two conditions for the tightness of the lower and upper bounds are established. An illustrative example with two different controllers is presented to verify this method.