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Sampled‐data state feedback stabilization of a class of nonlinear systems based on Euler approximation
Author(s) -
Malik Fahad Mumtaz,
Malik Mohammad Bilal,
Munawar Khalid
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.233
Subject(s) - lipschitz continuity , nonlinear system , convergence (economics) , control theory (sociology) , euler's formula , trajectory , controller (irrigation) , mathematics , discrete time and continuous time , exponential function , exponential stability , class (philosophy) , sampling (signal processing) , computer science , control (management) , mathematical analysis , statistics , physics , filter (signal processing) , quantum mechanics , astronomy , artificial intelligence , agronomy , economics , computer vision , biology , economic growth
Abstract In this paper, sampled‐data control of locally Lipschitz nonlinear systems is studied. The controller is designed entirely in the discrete‐time domain. The design is based on the approximate discrete‐time model of the continuous‐time system obtained using the Euler method. The analyses of the closed loop system establish trajectory convergence, which implies asymptotic/exponential convergence for arbitrarily small sampling time. The major contribution of this paper is that asymptotic/exponential convergence of the closed loop system is proved under some additional conditions for a sufficiently small but nonzero sampling time. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society