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The present work establishes necessary and sufficient conditions for anonlinear system with two inputs to be described by a specific triangular form.Except for some regularity conditions, such triangular form is flat. This maylead to the discovery of new flat systems. The proof relies on well-knownresults for driftless systems with two controls (the chained form) and ongeometric tools from exterior differential systems. The paper also illustratesthe application of its results on an academic example and on a reduced ordermodel of an induction motor.

A Flat Triangular Form for Nonlinear Systems with Two Inputs: Necessary and Sufficient Conditions