EXERCISE:

Using the diagram in Figure $1,$ study the stability of the closed$-$loop system where the values $G_1(s)=\frac{1}{s+2}$ 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