A block triangular nonlinear observer normal form

Rudolph, Joachim; Zeitz, Μ.

doi:10.1016/0167-6911(94)90075-2

Cited by 82 publications

(62 citation statements)

References 8 publications

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“…Different notions of observability exist [6], [20], [23]. We take the definition which is based on uniquely defined observability indices and ensures a single normal form.…”

Section: B Problem Statementmentioning

confidence: 99%

“…Some of the extensions are achieved by eliminating constraints in the target normal forms. For instance, the block triangular observer form in [23] allows a more general dependence in the system's output injection vector. Other approaches apply immersion techniques or dynamic error linearization [17], [22], [1].…”

Section: Introductionmentioning

confidence: 99%

“…The well-established exact error linearization nonlinear observer design method uses an Observer Form (OF) to obtain stable Linear Time-Invariant (LTI) state estimate error dynamics in OF coordinates [14], [2]. Significant effort has been placed on extending this original work for single-output continuous-time systems [15], [25], [7], [23], [18], [11], [13], [19], [16], [3]. Some of the extensions are achieved by eliminating constraints in the target normal forms.…”

Section: Introductionmentioning

confidence: 99%

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On the Output Transformation to an Observer Form

Wang

Lynch

Bortoff³

2010

IASTED Technology Conferences / 696:MS / 697:CA / 698: WC / 699: EME / 700: SOE

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This paper investigates the transformability of an unforced multi-output nonlinear system to a multi-output observer form. The existence conditions of an output transformation and a change of state coordinates are presented in a more concise form than those given in literatures. Given an output transformation, verifying these conditions can reveal if the unforced system is transformable to the observer form. Necessary conditions on the output transformation are given for the single output and multi-output nonlinear systems. These necessary conditions are stated as a set of first order partial differential equations, which are relatively easy to solve and potentially useful to obtain the output transformation candidates. The 12th IASTED International Conference on Control and ApplicationsThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. MERLCoverPageSide2On the output transformation to an observer form Yebin Wang, Alan F. Lynch, and Scott A. BortoffAbstract-This paper investigates the transformability of an unforced multi-output nonlinear system to a multi-output observer form. The existence conditions of an output transformation and a change of state coordinates are presented in a more concise form than those given in literatures. Given an output transformation, verifying these conditions can reveal if the unforced system is transformable to the observer form. Necessary conditions on the output transformation are given for the single output and multi-output nonlinear systems. These necessary conditions are stated as a set of first order partial differential equations, which are relatively easy to solve and potentially useful to otain the output transformation candidates.

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“…Different notions of observability exist [6], [20], [23]. We take the definition which is based on uniquely defined observability indices and ensures a single normal form.…”

Section: B Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Output Transformation to an Observer Form

Wang

Lynch

Bortoff³

2010

IASTED Technology Conferences / 696:MS / 697:CA / 698: WC / 699: EME / 700: SOE

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“…On the other hand, owing to the fact that it is easier to design an observer for linear systems, the natural approach to designing nonlinear observers, adopted by several researchers [15,25,22,14,12,1,2], consist in transforming the original system into i) either a linear one plus a nonlinear part having some special structures ii) or a linear one plus a nonlinear part depending only on the input and the output so the observer has linear error dynamics.…”

Section: Introductionmentioning

confidence: 99%

Observabilty singularities and observer design: dual immersion approach

et al. 2016

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It is well-known that, for nonlinear systems, the observability is often only a local property and depends on the input. Moreover, it is often required that the observer be of the same dimension as the original system. A direct consequence of this requirement is that it enlarges the set of observability singularities. If, on one hand, it is impossible to observe the state variables that are structurally unobservable, it is, however, possible to overcome the observability singularities introduced by the constraints on the observer design. In this paper, we propose a novel dual immersion method which allows to reduce the set of observability singularities. In addition, a step by step design of a high order sliding mode observer based on the proposed dual immersion approach is presented. Finally, a thorough analysis and discussion on the simulation results with respect to a non-autonomous system is given.

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“…These conditions are mainly difficult to apply to large scale systems because they are based on the computation of the rank of the observability matrix. Note that some studies assume that the system can be transformed into some triangular form which ensures the uniform observability and which is used in the design of nonlinear observers [2,7,14,19].…”

Section: Introductionmentioning

confidence: 99%

Uniform Observability Analysis for Structured Bilinear Systems A Graph-theoretic Approach

Boukhobza¹,

Hamelin²,

Sauter³

2006

European Journal of Control

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To cite this version:Taha Boukhobza, Frédéric Hamelin, Dominique Sauter. Uniform observability analysis for structured bilinear systems: A graph-theoretic approach. European Journal of Control, Lavoisier, 2006, 12 (5) Abstract This paper deals with the analysis of generic uniform observability for structured bilinear systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. We express, in graphical terms two conditions, the first one is necessary and the second one is sufficient, to check whether or not they are generically uniformly observable. These conditions are quite easy to verify because they are based on comparisons of integers and on finding edges and subgraphs in a digraph. Therefore, our approach is very well suited to study large scale and/or uncertain systems.

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A block triangular nonlinear observer normal form

Cited by 82 publications

References 8 publications

On the Output Transformation to an Observer Form

On the Output Transformation to an Observer Form

Observabilty singularities and observer design: dual immersion approach

Uniform Observability Analysis for Structured Bilinear Systems A Graph-theoretic Approach

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