Observer with linear error dynamics for nonlinear multi-output systems

Hou, M.; Pugh, A.C.

doi:10.1016/s0167-6911(98)00105-4

Cited by 108 publications

(50 citation statements)

References 14 publications

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“…Such observers are known as high-gain observers (e.g., [4,5]). In a third approach the nonlinear system is transformed into a linear one by an appropriate change of coordinates [6][7][8]. The estimate is computed in these new coordinates and the original coordinates are retrieved through the inverse transformation.…”

Section: Introductionmentioning

confidence: 99%

Design of a Nonlinear Finite-Time Converging Observer for a Class of Nonlinear Systems

Sauvage

Guay

Dochain

2007

Journal of Control Science and Engineering

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This paper proposes a nonlinear finite-time converging observer for a class of nonlinear systems. The estimate is recovered from the present and delayed estimates provided by two independent dynamical systems converging to a function of the state with linear error dynamics. The estimation is carried out using only the Jacobian matrix of both transformations determined by solving two systems of partial derivative equations. The results are illustrated on a bioreactor model.

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Section: Introductionmentioning

confidence: 99%

Design of a Nonlinear Finite-Time Converging Observer for a Class of Nonlinear Systems

Sauvage

Guay

Dochain

2007

Journal of Control Science and Engineering

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“…2) α i j is non-unique, because (6) and (7) are not sufficient to grantee the uniqueness. This non-constructive feature of Theorem 3.1 is result from the lack of necessary connection between α and the system dynamics f (x).…”

Section: Existence Conditionsmentioning

confidence: 99%

“…From simplicity, we take α (6) and (7). Solving (9) gives the output transformation ψ 1 = 1/ (b 1 − b 3 y 1 ).…”

Section: A Perspective System Examplementioning

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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“…[11] gave the sufficient and necessary conditions to solve the linearization problem for multi-output nonlinear systems. After these two important works in the field of observers, other interesting research was followed, we can quote for examples: [1], [2], [4], [10]. Even if the results, obtained in the works quoted above, can be used for multi-output linear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%