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

## TL;DR

This paper develops a robust state-feedback control method to asymptotically stabilize coupled nth-order differential systems despite unbounded, high-frequency oscillating perturbations, extending classical control results to broader perturbation classes.

## Contribution

It introduces a novel control design that ensures stability under unbounded, high-frequency oscillations, broadening the scope of existing control theory results.

## Key findings

- Achieved uniform asymptotic stabilization despite unbounded perturbations
- Extended classical control results to more general perturbation classes
- Proved limitations for perturbations depending only on time

## Abstract

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, $w=w(t).$