  This paper deals with an analysis and design of robust, state-feedback
control law uniform-asymptotically stabilizing at origin the system consisting
of coupled $n$th--order ordinary differential equations in the presence of a
non-vanishing at $x=0$ or even unbounded on the time interval $[0,\infty)$
time-varying high-frequency oscillating perturbation $w(t,x).$ The obtained
results generalize and extend some known and now classical results in the
control theory for a wider class of perturbations. Moreover, as is shown in the
paper, there is no room for further generalization for $w$ which is
time-dependent only, $w=w(t).$
