Characterization of accessibility for a class of nonlinear time-delay systems

The accessibility of the class of driftless single-input nonlinear time-delay systems is fully characterized for the first time. This result is obtained through the introduction of new tools within a geometric approach recently introduced in the literature. Moreover, all those possible autonomous elements, which can depend on the variables with time-delay, are also characterized when the system is not accessible and in consequence, a canonical form of those systems is deduced.