\chapter{Math Background}
\begin{example} \rm
We use the generalized Bellman-Gronwall lemma to determine $k^* \ge 0$ such that for any $k \ge k^*$ the system
\[
\dot{\b x}(t)={\b A \b x}(t)+{\b f}(t,{\b x}(t)), \quad{\b x}(0)={\b x}_0,
\]
is globally uniformly asymptotically stable for any ${\b f}(t,{\b x}(t))$ for which $\|{\b f}(t,{\b x}(t))\|_2 < k\|{\b x}\|_2$, where ${\b A}$ is asymptotically stable.
\end{example}



