1. Min-switching local stabilization for discrete-time switching systems with nonlinear modes
- Author
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Marc Jungers, Jamal Daafouz, Carlos Alberto Cavichioli Gonzaga, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Lyapunov function ,0209 industrial biotechnology ,Optimization problem ,Quadratic lyapunov function ,02 engineering and technology ,Domain (mathematical analysis) ,[SPI.AUTO]Engineering Sciences [physics]/Automatic ,symbols.namesake ,020901 industrial engineering & automation ,0203 mechanical engineering ,Control theory ,Min-switching local stabilization ,Basin of attraction estimate ,Cone bounded nonlinearity ,Mathematics ,020301 aerospace & aeronautics ,Lyapunov-Metzler inequalities ,Input saturation ,Maximization ,Computer Science Applications ,Nonlinear system ,Modal ,Discrete time and continuous time ,Control and Systems Engineering ,symbols ,Analysis - Abstract
International audience; 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.
- Published
- 2013
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