Convex invariant sets for discrete-time Lur'e systems

Teodoro Alamo (1) , A. Cepeda (2) , Mirko Fiacchini (1) , Eduardo Camacho (2)

1 ISA - Departamento de Ingenieria de Sistemas y Automatica [Sevilla]
2 ISA - Department of Automatic Control and Systems Engineering [Sevilla]

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.

Mots clés: Set invariance Domain of attraction Lur'e systems

Domaines: Systèmes dynamiques [math.DS]

Teodoro Alamo, A. Cepeda, Mirko Fiacchini, Eduardo Camacho. Convex invariant sets for discrete-time Lur'e systems. Automatica, 2009, 45 (4), pp.1066-1071. ⟨10.1016/j.automatica.2008.11.013⟩. ⟨hal-00968209⟩