  A nonsmooth extension of the speed-gradient algorithms in finite form is
proposed. The conditions ensuring control goal (convergence of the goal
function to zero) are established. A new algorithm is applied to almost global
stabilization of the Brockett integrator that has become a popular benchmark
for nonsmooth and discontinuous algorithms. It is proved that the designed
control law stabilizes the Brockett integrator for any initial point that does
not lie on the x3-axis. Besides, it is shown that the speed-gradient algorithm
ensures stabilization with an arbitrarily small control level. An important
feature of the proposed control is the fact that it is continuous along
trajectories of the closed-loop system.
