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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 nonpolynomial 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.

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.

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