Replace an analog controller $4\frac{s+2}{s+4}$ with a digital controller using Tustin's approximation. The plant transfer function is given below.

$1$

$G(s)=$

$--,H(s)=1$

$s(s+1)$

Find the largest sampling time, $T_1,$ for which closedloop system is stable. Please have a discussion of simulation results in your repot. Submit a Simulink file which can on MATLAB R$2023$a$.$ Show plots of output, $y(t),$ for analog controller and digital controller for $T=0\mathrm{.}25,T=0\mathrm{.}5,$ and $T=T_1$ on the same graph.