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Local Input-Output Decoupling of Discrete Time Nonlinear Systems

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Algebraic and Geometric Methods in Nonlinear Control Theory

Part of the book series: Mathematics and Its Applications ((MAIA,volume 29))

Abstract

A local treatment of the (restricted) block input-output decoupling problem is given. The major tools employed are the invariant and locally controlled invariant distributions which have recently been extended to the discrete time domain.

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References

  1. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, 2nd ed., Springer-Verlag, New York, Applications of Mathematics, 1979.

    MATH  Google Scholar 

  2. A. S. Morse and W. M. Wonham, ‘Status of Non-interacting Control,’ IEEE Trans, on Automatic Control, Vol. AC-16, 1971, pp. 568–581.

    Article  MathSciNet  Google Scholar 

  3. P. K. Sinha, ‘State Feedback Decoupling of Nonlinear Systems,’ IEEE Trans, on Automatic Control, Vol. AC-22, 1977, pp. 487–48–9.

    Article  Google Scholar 

  4. D. Claude, ‘Découplage des systèmes non linéaires, séries génératrice non commutative et algébres de Lie,’ SIAM J. of Control, to appear.

    Google Scholar 

  5. A. Isidori, A. J. Krener, C. Gori-Giorgio, and S. Monaco, ‘Nonlinear Decoupling via Feedback: A Differential Geometric Approach,’ IEEE Trans, on Automatic Control, Vol. AC-26, No. 2, April 1981, pp. 331–345.

    Article  Google Scholar 

  6. N. Nijmeijer and J. M. Schumacher, ‘The Noninteracting Control Problem for Nonlinear Control Systems,’ Memo 427, Dept. Appl. Math., Twente University of Technology, May 1983.

    Google Scholar 

  7. A. J. van der Schaft, ‘Linearization and Input-Output Decoupling for General Nonlinear Systems,’ Systems and Control Letters, Vol. 5, 1985. pp. 27–33.

    Google Scholar 

  8. J. W. Grizzle, ‘Controlled Invariance for Discrete Time Nonlinear Systems with an Application to the Disturbance Decoupling Problem,’ IEEE Trans, on Automatic Control, to appear.

    Google Scholar 

  9. J. W. Grizzle, ‘Distributions invariantes commandées pour les systèmes non linéaires en temps discret,’ Comptes Rendus de L’Acad Emie des Sciences, Paris, t. 300, Serie I, No. 13, 1985, pp. 447–450.

    Google Scholar 

  10. S. Monaco and D. Normand-Cyrot, ‘Sur la commande non interactive des systèmes non linéaires en temps discret,’ in Lecture Notes in Control and Information Science, Springer-Verlag, Vol. 63, edited by A. Bensoussan and J. L. Lions, Nice, June 19–22, 1984, pp. 364–377.

    Google Scholar 

  11. S. Monaco and D. Normand-Cyrot, ‘Invariant Distributions for Discrete-Time Nonlinear Systems,’ Systems and Control Letters, Vol. 5, No. 3, pp. 191–196.

    Google Scholar 

  12. J. W. Grizzle, ‘Decoupling of Discrete Time Nonlinear Systems,’ to appear in Int. J. of Control.

    Google Scholar 

  13. W. Respondek, ‘On Decomposition of Nonlinear Control Systems,’ Systems and Control Letters, Vol. 1, 1982, pp. 301–308.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. W. Grizzle and H. Nijmeijer, ‘Zeros at Infinity for Nonlinear Discrete Time Systems,’ to appear in Int. J. of Math. Syst. Thy.

    Google Scholar 

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© 1986 D. Reidel Publishing Company

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Grizzle, J.W. (1986). Local Input-Output Decoupling of Discrete Time Nonlinear Systems. In: Fliess, M., Hazewinkel, M. (eds) Algebraic and Geometric Methods in Nonlinear Control Theory. Mathematics and Its Applications, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4706-1_22

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  • DOI: https://doi.org/10.1007/978-94-009-4706-1_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8593-9

  • Online ISBN: 978-94-009-4706-1

  • eBook Packages: Springer Book Archive

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