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Maximal feedback linearization with internal stability over ℝ4

Nonlinear systems over ℝ4 include celebrated mechanical systems as the Acrobat, the Pendubot, the Ball and Beam, the invertible wheel pendulum. This paper derives general results for the classification of accessible single-input systems over ℝ4. Those results are instrumental for the stabilization: according to structural properties, a dummy output function is computed, whenever it exists, with asymptotically stable zero dynamics.