  This paper focuses on the problem of constructing time-varying feedback laws
that asymptotically stabilize a given part of the state variables for nonlinear
control-affine systems. It is assumed that the class of systems under
consideration satisfies nonlinear controllability conditions with respect to
the stabilizable variables. Under these assumptions, a time-periodic feedback
control is constructed explicitly by using the inversion of the matrix composed
of the control vector fields and their Lie brackets. The proposed control
design scheme is applied to solving the leader-following problem for nonlinear
multi-agent systems. These results are illustrated with two examples of
nonholonomic control problems: the partial stabilization of a rolling disc and
the leader-following task for two unicycles.
