Chapter 6.3, Problem 16P

Find constant $4\times 1$ vectors ${\text{u}}_{\text{1}}{\text{,u}}_{\text{2}},$ and ${\text{u}}_{\text{3}}$ such that the solution of the initial value problem

$\text{x}\text{'}=\left(\begin{array}{cccc}1& 5& 3& -5\\ 2& 3& 2& -4\\ 0& -1& -2& 1\\ 2& 4& 2& -5\end{array}\right)\text{x,}\text{x}\left(0\right)={\text{x}}_0$

tends to ${\left(\begin{array}{cccc}0& 0& 0& 0\end{array}\right)}^T$ as $t\to \infty$ for any ${\text{x}}_{\text{0}}\in S$, where

$S=\left\{\text{u:u}=a_1{\text{u}}_1+a_2{\text{u}}_{\text{2}}+a_3{\text{u}}_{\text{3}},-\infty <a_1,a_2,a_3<\infty \right\}$.