  In this paper, we present a generalization of the super-twisting algorithm
for perturbed chains of integrators of arbitrary order. This Higher Order
Super-Twisting (HOST) controller, which extends the approach of Moreno and
als., is homegeneous with respect to a family of dilations and can be
continuous. Its design is derived from a first result obtained for pure chains
of integrators, the latter relying on a geometric condition introduced by the
authors. The complete result is established using a homogeneous strict Lyapunov
function which is explicitely constructed. The effectiveness of the controller
is finally illustrated with simulations for a chain of integrator of order
four, first pure then perturbed, where we compare the performances of two HOST
controllers.
