Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems

In the last fifteen years a theory for nonlinear control systems has been developed using differential geometric methods. Many problems have been treated 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 survey and bibliography. We want to emphasize only that in most of the papers devoted to nonlinear control systems (using geometric methods) only a local viewpoint is presented. This is due to two kinds of obstructions: singularities of the studied objects (functions, vector fields, distributions) and topological obstructions for the global existence of the sought solutions.

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