This paper presents a feedback control scheme for the stabilization of
two-input, driftless, chained nonholonomic systems, also called chain
ed form. These systems are controllable but not asymptotically stabili
zable by a smooth static-state feedback control law. In addition, expo
nential stability cannot be obtained with a smooth, time-varying feedb
ack control law, Here, global, asymptotical stability with exponential
convergence is achieved about any desired configuration by using a no
nsmooth, time-varying feedback control law. The control law depends, i
n addition to the state and time, on a function which is constant exce
pt at predefined instants of time where the function is recomputed as
a nonsmooth function of the state. The inputs are differentiable with
respect to time and tend exponentially toward zero. For use in the ana
lysis, a lemma on the exponential convergence of a stable time-varying
nonlinear system perturbed by an exponentially decaying signal is pre
sented. Simulation results are also shown.