On dynamic feedback linearization in R4

The authors discuss the problem of dynamic feedback linearization for a nonlinear system in R⁴ with two independent controls: the problem is to determine a dynamic compensator so that the closed loop can be expressed as a linear controllable system in suitable local coordinates in the extended state space. The results so far available give a complete characterization of control systems in R³ and of control systems in which the number of independent controls is equal to the number of states minus one. For general systems necessary and sufficient conditions have been given, but examples in R⁴ with two controls already show a gap between necessity and sufficiency. This gap is discussed