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H∞ Filter Design for Classes of Nonlinear Systems Open Access


Other title
Lipschitz Nonlinear Systems
Linear Matrix Inequality
One-sided Lipschitz Nonlinear Systems, Lipschitz Nonlinear Systems, Linear Matrix Inequality, Filter Design
One-sided Lipschitz Nonlinear Systems
Filter Design
Type of item
Degree grantor
University of Alberta
Author or creator
Movahhedi, Omid
Supervisor and department
Horacio, J. Marquez (Department of Electrical and Computer Engineering)
Examining committee member and department
Yasser, Abdel-Rady I. Mohamed (Department of Electrical and Computer Engineering)
Jinfeng, Liu (Department of Chemical and Materials Engineering)
Horacio, J. Marquez (Department of Electrical and Computer Engineering), Jinfeng, Liu (Department of Chemical and Materials Engineering), Yasser, Abdel-Rady I. Mohamed (Department of Electrical and Computer Engineering)
Horacio, J. Marquez (Department of Electrical and Computer Engineering)
Department of Electrical and Computer Engineering
Date accepted
Graduation date
Master of Science
Degree level
Estimation of internal states of nonlinear systems has been a wide area of interest in recent years for control design and online processing. According to the difficulty of setting up sensors and also the cost they impose for implementation, estimation of these states would decrease the operation cost of the industrial systems. Nonlinear filter design for two classes of systems known as Lipschitz and one-sided Lipschitz is presented in this thesis. Filter design for Lipschitz nonlinear systems is investigated in discrete-time and one-sided Lipschitz nonlinear systems in continuous-time. One-sided Lipschitz systems represent an extension of the well known class of Lipschitz systems that has been used in the control literature for the past four decades. We present a complete solution of the filtering problem when the noise sources have bounded energy, i.e., we solve the synthesis of the so-called H∞ filter that minimize the effect of disturbances over the estimates. Our solution will be shown to be robust with respect to parametric and unstructured nonlinear uncertainties. In the case of Lipschitz nonlinear systems, missing information and delayed measurement is modelled and the sufficient condition under which the filter design is asymptotically stable is presented. The problem is then formulated in terms of Linear Matrix Inequalities (LMIs) which can be easily solved using commercial software packages.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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