Titlebook: Algebraic and Geometric Methods in Nonlinear Control Theory; M. Fliess,M. Hazewinkel Book 1986 D. Reidel Publishing Company, Dordrecht, Ho

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Realizations of Polynomial Systems been interested in immersions of nonlinear systems into polynomial ones (immersions into simpler systems as affine or linear ones have been studied by Fliess and Kupka [4], Claude, Pliess and Isidori [2] and Claude [3]. The observation algebra of a nonlinear system has appeared to be a useful tool

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Symmetries and Local Controllability related to the existence of certain symmetries, including results by the authors and H. J. Sussmann. We also comment on the relation between this work and generalizations of Lie group theory to semigroups and Lie wedges.

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Original

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Everything You Always Wanted to Know about Linearizationrds. Then, as geometrical methods appeared, the 70’s yielded a sound knowlegde of autonomous linear systems (cf. Wonham [66]) while, with the introduction of differential geometry thanks to Hermann [30] and Lobry [44] in particular, nonlinear automatic control actually emerged (*).

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Feedback Linearization and Simultaneous Output Block Decoupling of Nonlinear Systemshe largest controllability distributions contained in . are linearly independent, for a nonlinear system to be feedback linearized and output block decoupled it is necessary and sufficient that the algorithm is executable. This algorithm, is novel in the sense that there are no constraints on the nu

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Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Contted in this fashion and interesting results have been obtained for nonlinear equivalence, decomposition, controllability, observability, optimality, synthesis of control (with desired properties: decoupling or noninteracting), linearization and many others. We refer the reader to Sussmann [28] for a

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The Extended-Linearization Approach for Nonlinear Systems Problemse used, yielding a system whose linearization has the desired characteristics. So long as the resulting system is operated in a region sufficiently close to the nominal operating point, the linearization should accurately reflect the behavior of the nonlinear system. Of course, simulation is used to