Consider the following nonlinear perturbed dynamical system:
$\dot{x} = f(t,x)+g(t,x)$,
such that $x \in \mathbb{R}^n$, $g(t,x)$ is a perturbation term such that
$g(t,0) = 0$
and
$x=0$ is an uniformly asymptotically stable equilibrium point of the nominal system
$\dot{x} = f(t,x)$.
Consider also that $g(t,x)$ has a polynomial form in $x$ of order N.
With the information given, can you take any conclusions about the stability of the zero equilibrium point of the nonlinear perturbed system?