# scipy.signal.tf2ss¶

scipy.signal.tf2ss(num, den)[source]

Transfer function to state-space representation.

Parameters
num, denarray_like

Sequences representing the coefficients of the numerator and denominator polynomials, in order of descending degree. The denominator needs to be at least as long as the numerator.

Returns
A, B, C, Dndarray

State space representation of the system, in controller canonical form.

Examples

Convert the transfer function:

$H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}$
>>> num = [1, 3, 3]
>>> den = [1, 2, 1]


to the state-space representation:

\begin{align}\begin{aligned}\begin{split}\dot{\textbf{x}}(t) = \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\\end{split}\\\textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)\end{aligned}\end{align}
>>> from scipy.signal import tf2ss
>>> A, B, C, D = tf2ss(num, den)
>>> A
array([[-2., -1.],
[ 1.,  0.]])
>>> B
array([[ 1.],
[ 0.]])
>>> C
array([[ 1.,  2.]])
>>> D
array([[ 1.]])


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