The TF control approach find natural applications in the domain of mechanical vehicles, as illustrated by the examples pointed out along these pages. But the approach may also apply to other types of systems.

For instance, in a paper presented at the 2003 IEEE Conference on Decision and Control (CDC), a singularity-free version of the field-oriented control method is derived by applying the TF control approach to the Park’s two-phase equivalent model of an induction motor. For the sake of simplification, the two stator currents are taken as control inputs. This is justified by the fact that corresponding control voltages can be calculated via a classical backstepping procedure. A third control input is the time-derivative of the variable on which the used transverse function depends. The proposed control design relies on the fact that the Park’s model can be written in the form of a locally controllable driftless nonlinear system that is left-invariant on a Lie group, subjected to an additive vector-field here viewed as a perturbation. This driftless nonlinear system is itself equivalent to the three dimensional chained system used to model a nonholonomic cart.