Consider the following matrices.

$A=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& -1\end{array}\right],B=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right],C=\left[\begin{array}{ccc}1& 0& 0\end{array}\right],D=2.$

Now, for each of the following systems, determine if the system is uniformly stable $($US$),$ uniformly asymptotically stable $($UAS$),$ bounded$-$input bounded$-$state $($BIBS$)$ stable and bounded$-$input bounded$-$output $($BIBO$)$ stable.

a$)$ A continuous$-$time system where $A,B,C$ and $D$ are given above

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

$y(t)=Cx(t)+Du(t)$

b$)$ A discrete$-$time system where $A,B,C$ and $D$ are given above

$x[k+1]=Ax[k]+Bu[k]$

$y[k]=Cx[k]+Du[k]$