# scipy.signal.tf2ss

scipy.signal.tf2ss(num, den)

  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.

  Returns
    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:

  \[ \begin{align}\begin{aligned}\begin{split}\dot{\textbf{x}}(t) = \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\\end{split}\\\textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)\end{aligned}\end{align} \]

      >>> 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.]])

scipy.signal.tf2sos scipy.signal.zpk2tf