I have this 2nd order transfer function: $$G(s) = \frac{2}{s} + \frac{1}{s+2}$$
And I need to find a possible state space representation in the form of:
$$ \frac{dx}{dt} = Ax + bu $$ $$y = c^Tx$$
Matrix A
Matrix A is the system matrix, and relates how the current state affects the state change x' . If the state change is not dependent on the current state, A will be the zero matrix. The exponential of the state matrix, eAt is called the state transition matrix.
Matrix B
Matrix B is the control matrix, and determines how the system input affects the state change. If the state change is not dependent on the system input, then B will be the zero matrix.
Matrix C
Matrix C is the output matrix, and determines the relationship between the system state and the system output.
I can see the eigenvalues, they are $s_1 = 0$ and $s_2 = -2$.
So I can write down a diagonal matrix like that I think:
$$ A = \begin{pmatrix} 0 & 0 \\0 & -2 \end{pmatrix}
$$
But know I am stuck.
Is there some sort of trick I can use?