Repeat Problem 8.5 considering \(G(s)=\left(s^{2}+s+4ight)^{-1}\).

Data From Problem 8.5

Consider an open loop system having a transfer function \(G(s)=\) \(\left(s^{2}+4ight)^{-1}\) and a sampler placed before \(G(s)\). Find its output \(c(t)\) by the conventional \(z\)-transform analysis for a sampling period \(h=0.1 \mathrm{~s}\) with a unit step input. Also, determine the output of the system via \(\delta\)-domain DOTF approach. Consider \(m=10\) and \(T=1 \mathrm{~s}\).

Compare the results obtained by two methods of analysis by estimating the percentage errors.