scipy.signal.

ss2tf#

scipy.signal.ss2tf(A, B, C, D, input=0)[source]#

State-space to transfer function.

A, B, C, D defines a linear state-space system with p inputs, q outputs, and n state variables.

Parameters:

Aarray_like: State (or system) matrix of shape (n, n)
Barray_like: Input matrix of shape (n, p)
Carray_like: Output matrix of shape (q, n)
Darray_like: Feedthrough (or feedforward) matrix of shape (q, p)
inputint, optional: For multiple-input systems, the index of the input to use.

Returns:

num2-D ndarray: Numerator(s) of the resulting transfer function(s). num has one row for each of the system’s outputs. Each row is a sequence representation of the numerator polynomial.
den1-D ndarray: Denominator of the resulting transfer function(s). den is a sequence representation of the denominator polynomial.

Notes

Before calculating num and den, the function abcd_normalize is called to convert the parameters A, B, C, D into two-dimesional arrays. Their dtypes will be “complex128” if any of the matrices are complex-valued. Otherwise, they will be of type “float64”.

The State-space system representation section of the SciPy User Guide presents the corresponding definitions of continuous-time and disrcete time state space systems.

Array API Standard Support

ss2tf has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	⛔
PyTorch	⛔	⛔
JAX	⛔	⛔
Dask	⛔	n/a

See Support for the array API standard for more information.

Examples

Convert the state-space representation:

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

>>> A = [[-2, -1], [1, 0]]
>>> B = [[1], [0]]  # 2-D column vector
>>> C = [[1, 2]]    # 2-D row vector
>>> D = 1

to the transfer function:

\[H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}\]

>>> from scipy.signal import ss2tf
>>> ss2tf(A, B, C, D)
(array([[1., 3., 3.]]), array([ 1.,  2.,  1.]))