A continuous-time LTI System at rest has the following State and Output Equations in matrix form,
$\begin{bmatrix} \dot{x}_1 \\ \dot{x}_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -4 & -5 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ 1 \end{bmatrix} u_m$
y = [1 0]$ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$
The State Response to a unit step, ($u_{in}(t) = u(t)$), in the time domain, can be given as (calculate a, b, c, d, e, using only integers or simplified fractions, no
decimals allowed in this exercise).
$x(t) = \begin{bmatrix} a+be^{-t}+ce^{-4t} \\ d+e^{-t}+ee^{-4t} \end{bmatrix} u(t)$
a =
b =
c =
d =
e =