PROBLEM: Design an integral controller for the plant
\dot{x}=\left[\begin{matrix} 0 & 1 \\ -7 & -9 \end{matrix} \right] x+\left[\begin{matrix} 0 \\ 1 \end{matrix} \right] uy=\left[\begin{matrix} 4 & 1 \end{matrix} \right] x
to yield a step response with 10% overshoot, a peak time of 2 seconds, and zero steady-state error.