Consider a continuous$-$time LTI state$-$space equation as

$x^{}(t)=Ax(t)$

where the matrix $A$ is given by

$A=\left[\begin{array}{cccc}-1& 1& 1& -3\\ 3& -2+k& 2& 2\\ 2& 0& k& 1\\ 3& -2& -1& -2\end{array}\right]$

Here kinR is a design parameter. Using Lyapunov stability theory, fund a range of value for $k$ so that the system is guaranteed to be UES.