Laplace Transform

We usually take the Laplace transform of this plant to work in the frequency domain.

$$\mathcal{L}={\int }_0^{\infty }x(t)e^{-st}dt$$

The Inverse Laplace Transform is given by

$$x(t)={\mathcal{L}}^{-1}\{X(s)\}=\frac{1}{2\pi j}{\int }_{\sigma -j\infty }^{\sigma +j\infty }X(s)e^{st}ds$$

Following that, we can take the Laplace Transform of the dynamical system.