Existence of equilibrium point under asymptotically vanishing disturbance

Question

Consider an autonomous dynamical system $\dot{x}=f(x)$ and suppose that we know that the solutions converge to a limiting set of equilibrium points $\Omega$ in $\mathbb{R}^n$. Consider now the perturbed dynamical system $\dot{x}=f(x)+d(t)$, where $\lim_{t\to\infty}d(t)=0$. Is it true that the solutions of the perturbed dynamical system converge to $\Omega$ too? If so, how can we prove it? Do we need any conditions on the set $\Omega$ or the function $f$ for this to hold? I haven't been able to find a counterexample.