Abstract
In this paper, the notion of SNS-domain of attraction is applied to the synthesis of saturated controllers. The notion of SNS-domain was first introduced in the framework of estimation of the domain of attraction of a discrete saturated control system. The main contribution of this paper is an algorithm that allows to obtain a saturated control law for a linear system maximizing the domain of attraction. The parameters of the controller are obtained in such a way that the size of the corresponding polyhedric SNS-domain of attraction is maximized. It is well known that, for single input systems, the greatest ellipsoidal invariant set can be obtained by means of a control law that does not saturate in the corresponding ellipsoidal set. In this paper it is shown how saturated control laws yield to greater domain of attractions when polyhedric invariant sets are considered. That is, the algorithm proposed in this paper provides a controller with a domain of attraction that contains any pre-specified ellipsoidal control invariant set obtained by means of a non saturated control law.
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