On Goursat normal forms, prolongations, and control systems

In this paper, the method of exterior differential systems for analyzing nonlinear systems is presented. Conditions are given for converting Pfaffian systems into Goursat normal form, and for converting control systems into Brunovsky form. All of the existing results on feedback linearization for control systems can be restated in the language of Pfaffian systems, and in addition, new conditions for linearizing control systems using dynamic extension are given.<
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