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A new concept of invariance for a class of discrete-time Lur’e systems: application to synthesis of robust saturated controllers.

A new concept of invariance for a class of Lur'e systems is presented. This new notion of invariance, denoted as LNL-invariance, has a number of geometrical properties that makes its use suitable for the estimation of the domain of attraction of this class of non-linear systems. The notion of LNL-domain of attraction, an estimation of the domain of attraction, is introduced. It is shown that, in case of single input Lur’e systems, any contractive set is contained in the LNL- domain of attraction. A simple algorithm that converges to the LNL-domain of attraction is presented. The adaptation of the concept of LNL-invariance to saturated systems (defined SNS-invariance) is applied to the synthesis of saturated controllers for multi-input systems. The notion of SNS-domain yields to an algorithm for computing a robust 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. Here 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.

Type of Seminar:
Ph.D. Seminar
Mirko Fiacchini
University of Sevilla, Spain
Nov 07, 2006   11:15

Building ETL, Room K 25
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Dr. Colin Jones
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