# scipy.signal.tf2ss¶

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

Transfer function to state-space representation.

Parameters: num, den : array_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. A, B, C, D : ndarray 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{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}$$\begin{split}\textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)\end{split}$
>>> 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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