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Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems
Author(s) -
Coutinho Daniel,
Souza Carlos E.
Publication year - 2012
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.2833
Subject(s) - nonlinear system , mathematics , lyapunov function , domain (mathematical analysis) , stability (learning theory) , class (philosophy) , control theory (sociology) , discrete time and continuous time , algebraic number , mathematical optimization , computer science , mathematical analysis , statistics , physics , control (management) , quantum mechanics , machine learning , artificial intelligence
SUMMARY This paper proposes a linear matrix inequality based method for the estimation of domain of attraction for a class of discrete‐time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete‐time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. Numerical examples illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.