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State-Affine Normal Forms

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Observer Design for Nonlinear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 479))

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Abstract

The standard state-affine normal forms are presented. We dissociate the ones having a stationary linear part for which a simple Luenberger observer can be used, and the ones having a time-varying linear part for which a Kalman design with a time-varying gain is necessary.

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Notes

  1. 1.

    In [1], the authors propose an observer for a more general form \(\dot{\xi } = A \, \xi + B(u,y)+G\rho (H\xi )\), \(y = C \, \xi \), under certain conditions on \(\rho \).

  2. 2.

    If (A, C) is observable, the eigenvalues of \(A-KC\) can be chosen arbitrarily.

  3. 3.

    See Definition 2.1.

  4. 4.

    See Definition 2.1.

  5. 5.

    See Definition 2.1.

References

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  4. Hammouri, H., Morales, J.D.L.: Observer synthesis for state-affine systems. In: IEEE Conference on Decision and Control, pp. 784–785 (1990)

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  5. Kalman, R.: Contributions to the theory of optimal control. In: Conference on Ordinary Differential Equations (1960)

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Authors and Affiliations

  1. Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”, University of Bologna, Bologna, Italy

    Pauline Bernard

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  1. Pauline Bernard
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Correspondence to Pauline Bernard .

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Bernard, P. (2019). State-Affine Normal Forms. In: Observer Design for Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 479. Springer, Cham. https://doi.org/10.1007/978-3-030-11146-5_3

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