\[K^* = 16K = (\sqrt{2})^* \Rightarrow K = 0.25 \Rightarrow s = -1 \pm j; -3 \pm j\]

\[G(z) = K\frac{z-1}{z}z\left\{\frac{1}{s(s+1)}\right\} = K\frac{z-1}{z}\left\{\frac{z}{z-1} - \frac{z}{z-0.368}\right\}\]

\[= K\left(1 - \frac{z-1}{z-0.368}\right) = \frac{0.632K}{z-0.368}\]