(a) Compute the poles and zeros of the discrete-time systems that result from discretising the continuous-time system with transfer function

\[G(s)=\frac{10\left(s^{2}+0.2 s+2ight)}{\left(s^{2}+0.5 s+1ight)(s+10)}\]

for sampling intervals ranging from \(T_{s}=1 \mathrm{sec}\) to \(T_{s}=0.01 \mathrm{sec}\).

(b) Create a root locus plot showing the evolution of the poles and zeros computed in part

(a) as a function of \(T_{s}\).

(c) Repeat parts (a) and (b) for

\[G(s)=\frac{(s+0.1+2 i)(s+0.1-2 i)}{(s+0.1+i)(s+0.1-i)(s+0.1+0.5 i)(s+0.1-0.5 i)} .\]

(d) Repeat parts (a), (b), and

(c) for different discretisation methods.