PROBLEM: Design a linear state-feedback controller to yield 20% overshoot and a settling time of 2 seconds for a plant
G(s)=\frac{(s+6)}{(s+9)(s+8)(s+7)}that is represented in state space in cascade form by
\dot{z}= Az +Bu =\left[\begin{matrix} -7 & 1 & 0 \\ 0 & -8 & 1 \\ 0 & 0 & -9 \end{matrix} \right] z+\left[\begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right] uy = Cz = \left[\begin{matrix} -1 & 1 & 0\end{matrix} \right] z