A Characterization of the Lie Algebra Rank Condition by transverse periodic functions.
SIAM J. on Control and Optimization, vol 40: 1227-1249, 2001.
The Lie algebra rank condition plays a central role in nonlinear systems control theory. The present paper establishes that the satisfaction of this condition by a set of smooth control vector fields is equivalent to the existence of smooth transverse periodic functions. The proof here enclosed is constructive and provides an explicit method for the synthesis of such functions.