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Design of observers for nonlinear systems with H ∞ performance analysis
Author(s) -
Dong Yali,
Wang Hui,
Wang Yangang
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2830
Subject(s) - nonlinear system , mathematics , control theory (sociology) , observer (physics) , convergence (economics) , lyapunov function , lyapunov stability , stability (learning theory) , stability theory , computer science , control (management) , physics , quantum mechanics , artificial intelligence , machine learning , economics , economic growth
This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H ∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.