Robustness and Stability for Nonlinear Systems Decoupling and Feedback Linearization

  • B. Charlet
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)


We give some stability and robustness results for nonlinear systems which are transformed by feed-back and immersion into decoupled linear systems. In particular we give a necessary condition involving the Euler-Poincaré characteristic of asymptotic unobservable submanifolds. This condition is strictly weaker than the hypothesis of minimum phase introduced by Byrnes and Isidori ([2]), as shown by an example borrowed from robotics.


Robustness Stability Feedback decoupling and linearization Nonlinear system Immersion Euler-Poincaré characteristic. 


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  1. [1]
    V.I. ARNOLD: Equations différentielles ordinaires. Edition de Moscou, traduction française, 1974.zbMATHGoogle Scholar
  2. [2]
    C. BYRNES, A. ISIDORI: Asymptotic expansions, root-loci and the global stability of nonlinear feedback systems. in Alge-braic and Geometric Methods in Control Theory, M. Fliess, M. Hazewinkel Ed. Reidel Pub. Co. 1986.Google Scholar
  3. [3]
    D. CLAUDE: Decoupling of nonlinear systems, Syst. Contr. Letters, 1982, 242, 248.Google Scholar
  4. [4]
    D. CLAUDE, M. FLIESS, A. ISIDORI: Immersion directe et par bouclage d’un systbme non linéaire dans un linéaire. CRAS, t. 296, I, 1983, 237, 240.Google Scholar
  5. [5]
    B. D’ANDREA, J. LEVINE: C.A.O for nonlinear decoupling, perturbations rejection and feedback linearization with application to the dynamic control of a robot arm. in Algebraic and Geometric Methods in Contral Theory, M. Fliess, M. Hazewinkel Ed. Reidel Pub. Co. 1986.Google Scholar
  6. [6]
    C. GODBILLON: Eléments de Topologie Algébrique. Hermann, Paris 1971.zbMATHGoogle Scholar
  7. [7]
    A. ISIDORI, A. KRENER, C. GORI-GIORGI, S. MONACO: Nonlinear decoupling via feedback. IFFE Trans. AC. 26, 2, 1981, 331, 345.Google Scholar
  8. [8]
    A. KASINSKI, J. LEVINE: A fast graph-theoretic algorithm for the feedback decoupling problem of nonlinear systems. in Lect. Notes in Cont. and Inf. Sciences, 58, P.A. Fuhrmann Ed. Springer, 1984, 550, 562.Google Scholar
  9. [9]
    J. MILNOR: Topology from the Differential Viewpoint. The University Press of Virginia, Charlottesville, 1978.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • B. Charlet
    • 1
  1. 1.Centre d’Automatique et d’InformatiqueEcole Nationale Supérieure des Mines de ParisFontainebleau cedexFrance

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