Q$2$: Consider the system described by:

$x_1^{}=x_2,$;$x_1(0)=-4$

$x_2^{}=2x_1-x_2+4,$;$x_2(0)=4$

Find the opfimal control law a to Transfer the above system from given initial states to the origin while minimizes the follewing performance index :

$J={\displaystyle \underset{0}{\overset{T}{}}}[x_1^2+\frac{1}{2}{x}_2^2+\frac{1}{4}{u}^2]dt$

$e^{2t}=e^{-t}$