Brief paper: Convex invariant sets for discrete-time Lur'e systems

Authors:
T. Alamo;A. Cepeda;M. Fiacchini;E. F. Camacho
Affiliations:
Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain;Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain;Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain;Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

In this paper, a method to estimate the domain of attraction of a class of discrete-time Lur'e systems is presented. A new notion of invariance, denoted LNL-invariance, is introduced. An algorithm to determinate the largest LNL-invariant set for this class of systems is proposed. Moreover, it is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non-linear system. It is shown that any contractive set for the Lur'e system is contained in the LNL-invariant set obtained applying the results of this paper. Two illustrative examples are given.