Singularity in dynamic state feedback linearization

The dynamic state feedback linearization of a nonlinear system, using the special class of compensators proposed by Charlet-Levine-Marine (1991), referred to as prolongations, is considered. Generally dynamic state feedback linearizability is studied around the origin of the extended system state space and hence does not guarantee linearizability of the considered system around its “physical” origin, which involves only the original non-extended state variables. An attempt to shed light on this problem is given in the form of necessary conditions, which guarantee linearizability of a nonlinear system around the origin of the original state space, when dynamic state feedback linearizability in the extended state space is assured. Furthermore, sufficient conditions relating closely to those of dynamic state feedback linearizability via prolongations are given