Get zero, poles and gain from state space model? I'm going to transform a state space model:
$$\dot{x} = Ax + Bu \\ y = Cx + Du$$
Into a transfer function:
$$G(s) = \frac{Y(s)}{U(s)}$$
What I need is to find the zeros, poles and gain. Finding poles are really easy. I just find the eigenvalues of the matrix $A$.
$$det(sI-A) = 0$$
Then I get the poles $$s_i = a\Re_i + b\Im_i$$
But how about the gain and zeros? How do I find them?

This is a standard problem of finding the transfer function from a state-space model of a linear system. In particular, $\dot{x}=Ax+Bu \implies X(s)=(sI-A)^{-1}B U(s)$, and $y=Cx+Du \implies Y(s)=CX(s)+DU(s)$. Consequently,
$$Y(s) = CX(s) + D U(s) = (C(sI-A)^{-1}B +D)U(s) \implies G(s) = C(sI-A)^{-1}B +D.$$
Once you have $G(s)$, you can compute the poles, zeros etc. of the transfer function.
