Let the state vector be $x(t)=\left[\begin{array}{c}{x}_1(t)\\ x_2(t)\\ x_3(t)\\ x_4(t)\end{array}\right],$ where $x_1(t)=y(t),x_2(t)=\frac{dy(t)}{dt},x_3(t)=\frac{d^{2}y(t)}{d{t}^2},$ and $x_4(t)=\frac{d^{3}y(t)}{d{t}^3}.$ Convert the following differential equation into state$-$space representation $($state equation and output equation$).$ Here, let $u(t)$ be the input and $y(t)$ be the output.

$\frac{d^{4}y(t)}{d{t}^4}+2\frac{d^{3}y(t)}{d{t}^3}-5\frac{d^{2}y(t)}{d{t}^2}+4\frac{dy(t)}{dt}-7y(t)=-8u(t)$