Applications and Extensions of Goursat Normal Form to Control of Nonlinear Systems

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Richard M. Murray
Proceedings of the 32nd Conference on Decision and Control
December 1993

The Goursat normal form theorem gives conditions under which an Pfaffian exterior differential system is equivalent to a certain normal form. This paper details how the Goursat normal form and its extensions provide a unified framework for understanding feedback linearization, chained form, and differential flatness.

Keywords: Exterior differential systems, nonholonomic constraints, chained form, feedback linearization, differentially flat.