Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Marc Jungers (1) , Carlos Alberto Cavichioli Gonzaga (1) , Jamal Daafouz (1, 2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 IUF - Institut universitaire de France

This paper deals with the discrete-time switched Lur'e problem in finite domain. The aim is to provide a stabilization inside an estimate of the origin's basin of attraction, as large as possible, via a suitable switching rule. The design of this switching rule is based on the min-switching policy and can be induced by sufficient conditions given by Lyapunov-Metzler inequalities. Nevertheless instead of intuitively considering a switched quadratic Lyapunov function for this approach, a suitable switched Lyapunov function including the modal nonlinearities is proposed. The assumptions required to characterize the nonlinearities are only mode-dependent sector conditions, without constraints related to the slope of the nonlinearities. An optimization problem is provided to allow the maximization of the size of the basin of attraction estimate - which may be composed of disconnected sets - under the stabilization conditions. A numerical example illustrates the efficiency of our approach and emphasizes the specificities of our tools.

Mots clés: Min-switching local stabilization; Cone bounded nonlinearity; Input saturation; Basin of attraction estimate; Lyapunov-Metzler inequalities

Domaines: Automatique / Robotique

Marc Jungers, Carlos Alberto Cavichioli Gonzaga, Jamal Daafouz. Min-switching local stabilization for discrete-time switching systems with nonlinear modes. Nonlinear Analysis: Hybrid Systems, 2013, 9, pp.18-26. ⟨10.1016/j.nahs.2013.01.003⟩. ⟨hal-00786159⟩