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

nonlinear dynamics

Asymptotic stabilization of a system of coupled $n$th--order  differential equations with potentially unbounded high-frequency oscillating  perturbations