Using the diagram in Figure $1,$ study the stability of the closed$-$loop system where the

values G$\_(1)($s$)=(1)/($s$+2)$ and sampling period T$=0\mathrm{.}5$ seconds. Note, by study, the following

exercise should be carried out:

a$)$ Manually determine the closed loop transfer function in the Z domain and

determine stability.

b$)$ Using MATLAB programming determine the closed loop transfer function in the

Z domain and determine stability.

c$)$ Check the stability with respect to the sampling period T$.$

d$)$ Routh$-$Hurwitz criterion

Figure $1-$ Closed Loop System

PLEASE NOTE, CAN I PLEASE GET THE MATLAB PROGRAMMING AS WELL PLEASE.