Consider the system [left{begin{array}{l}dot{x}_{1} dot{x}_{2}end{array} ight}=left[begin{array}{cc}0 & 1 0 & -1end{array} ight]left{begin{array}{l}x_{1} x_{2}end{array} ight}+left[begin{array}{c}0 10end{array} ight] u, quad y=left[begin{array}{ll}1 & 0end{array} ight]left{begin{array}{l}x_{1} x_{2}end{array} ight}] a.

Consider the system

\[\left\{\begin{array}{l}\dot{x}_{1} \\\dot{x}_{2}\end{array}\right\}=\left[\begin{array}{cc}0 & 1 \\0 & -1\end{array}\right]\left\{\begin{array}{l}x_{1} \\x_{2}\end{array}\right\}+\left[\begin{array}{c}0 \\10\end{array}\right] u, \quad y=\left[\begin{array}{ll}1 & 0\end{array}\right]\left\{\begin{array}{l}x_{1} \\x_{2}\end{array}\right\}\]

a. Design a state-feedback controller, so that the closed-loop poles have a damping ratio \(\zeta=0.7\) and a natural frequency \(\omega_{n}=3 \mathrm{rad} / \mathrm{s}\).

b. \(A\) Verify the result in Part (a) by using the MATLAB command place.