PROBLEMS: For the plant
G(s)=\frac{100(s+10)}{s(s+3)(s+12)}represented in the state space in phase-variable form by
\dot{x} = Ax+Bu=\left[\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & -36 & -15 \end{matrix} \right] x+\left[\begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right] uy=Cx=\left[\begin{matrix} 1000 & 100 & 0\end{matrix} \right] x
design the phase-variable feedback gains to yield 5% overshoot and a peak time of 0.3 second.