Compute the gain of the system in steady state.

The function takes either 1, 2, 3, or 4 parameters:


A, B, C, D: array-like

A linear system in state space form.

Z, P, k: array-like, array-like, number

A linear system in zero, pole, gain form.

num, den: array-like

A linear system in transfer function form.

sys: LTI (StateSpace or TransferFunction)

A linear system object.


gain: matrix

The gain of each output versus each input: y = gain \cdot u


This function is only useful for systems with invertible system matrix A.

All systems are first converted to state space form. The function then computes:

gain = - C \cdot A^{-1} \cdot B + D