Invariant set \({\cal I}_{{\cal W}}\):
Suppose that there exist \(T=k\tau\) with \(k\in\mathbb{N}\),
and \(i\in\mathbb{N}\) such that:
\begin{equation}
B_{{\cal W}}((i+1)T) \subseteq B_{{\cal W}}(iT).
\end{equation}
where \(B_{\cal W}(t) = B(\tilde{x}(t), \delta_{\cal W}(t))\).
Then \({\cal I}_{{\cal W}}\equiv \bigcup_{t\in[0,T]} B_{{\cal W}}(iT+t)\) is a
compact (i.e., bounded and closed) invariant set containing, for \(t\in[iT,\infty)\), all the solutions \(x(t)\) of \(\Sigma\) with initial condition in \(B_0\).