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Global finite-time observers for a class of nonlinear systems
Thesis (PhD)--University of Pretoria, 2013.
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University of Pretoria
2014
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| _version_ | 1867613485542670336 |
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| access_status_str | Open Access |
| author2 | Xia, Xiaohua |
| author_browse | Xia, Xiaohua |
| author_facet | Xia, Xiaohua |
| collection | Thesis |
| dc_rights_str_mv | © 2013 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (PhD)--University of Pretoria, 2013. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/40825 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:36:53.925Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/40825 Global finite-time observers for a class of nonlinear systems Xia, Xiaohua liyunyan1984@163.com Li, Yunyan Finite-time observer Nonlinear system Incremental rate Rational powers High gain Homogeneity Finite-time stability Asymptotic stability Homogeneous Lyapunov function Lyapunov theory UCTD Thesis (PhD)--University of Pretoria, 2013. The contributions of this thesis lie in the area of global finite-time observer design for a class of nonlinear systems with bounded rational and mixed rational powers imposed on the incremental rate of the nonlinear terms whose solutions exist and are unique for all positive time. In the thesis, two different kinds of nonlinear global finite-time observers are designed by employing of finite-time theory and homogeneity properties with different methods. The global finite-time stability of both proposed observers is derived on the basis of Lyapunov theory. For a class of nonlinear systems with rational and mixed rational powers imposed on the nonlinearities, the first global finite-time observers are designed, where the global finite-time stability of the observation systems is achieved from two parts by combining asymptotic stability and local finitetime stability. The proposed observers can only be designed for the class of nonlinear systems with dimensions greater than 3. The observers have a dynamic high gain and two homogenous terms, one homogeneous of degree greater than 1 and the other of degree less than 1. In order to prove the global finite-time stability of the proposed results, two homogeneous Lyapunov functions are provided, corresponding with the two homogeneous items. One is homogeneous of degree greater than 1, which makes the observation error systems converging into a spherical area around the origin, and the other is of degree less than 1, which ensures local finite-time stability. The second global finite-time observers are also proposed based on the high-gain technique, which does not place any limitation on the dimension of the nonlinear systems. Compared with the first global finite-time observers, the newly designed observers have only one homogeneous term and a new gain update law where two new terms are introduced to dominate some terms in the nonlinearities and ensure global finite-time stability as well. The global finite-time stability is obtained directly based on a sufficient condition of finite-time stability and only one Lyapunov function is employed in the proof. The validity of the two kinds of global finite-time observers that have been designed is illustrated through some simulation results. Both of them can make the observation error systems converge to the origin in finite-time. The parameters, initial conditions as well as the high gain do have some impact on the convergence time, where the high gain plays a stronger role. The bigger the high gain is, the shorter the time it needs to converge. In order to show the performance of the two kinds of observers more clearly, two examples are provided and some comparisons are made between them. Through these, it can be seen that under the same parameters and initial conditions, although the amplitude of the observation error curve is slightly greater, the global finite-time observers with a new gain update law can make the observation error systems converge much more quickly than the global finite-time observers with two homogeneous terms. In the simulation results, one can see that, as a common drawback of high gain observers, they are noise-sensitive. Finding methods to improve their robustness and adaptiveness will be quite interesting, useful and challenging. gm2014 Electrical, Electronic and Computer Engineering unrestricted 2014-07-17T12:10:09Z 2014-07-17T12:10:09Z 2014-04-16 2013 Thesis Li, Y 2013, Global finite-time observers for a class of nonlinear systems, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/40825> D14/4/311/gm http://hdl.handle.net/2263/40825 en © 2013 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Finite-time observer Nonlinear system Incremental rate Rational powers High gain Homogeneity Finite-time stability Asymptotic stability Homogeneous Lyapunov function Lyapunov theory UCTD Global finite-time observers for a class of nonlinear systems |
| title | Global finite-time observers for a class of nonlinear systems |
| title_full | Global finite-time observers for a class of nonlinear systems |
| title_fullStr | Global finite-time observers for a class of nonlinear systems |
| title_full_unstemmed | Global finite-time observers for a class of nonlinear systems |
| title_short | Global finite-time observers for a class of nonlinear systems |
| title_sort | global finite time observers for a class of nonlinear systems |
| topic | Finite-time observer Nonlinear system Incremental rate Rational powers High gain Homogeneity Finite-time stability Asymptotic stability Homogeneous Lyapunov function Lyapunov theory UCTD |
| url | http://hdl.handle.net/2263/40825 |