scipy.signal.

StateSpace#

class scipy.signal.StateSpace(*system, **kwargs)[source]#

Linear Time Invariant system in state-space form.

Represents the system as the continuous-time, first order differential equation \(\dot{x} = A x + B u\) or the discrete-time difference equation \(x[k+1] = A x[k] + B u[k]\). StateSpace systems inherit additional functionality from the lti, respectively the dlti classes, depending on which system representation is used.

Parameters:
*system: arguments

The StateSpace class can be instantiated with 1 or 4 arguments. The following gives the number of input arguments and their interpretation:

dt: float, optional

Sampling time [s] of the discrete-time systems. Defaults to None (continuous-time). Must be specified as a keyword argument, for example, dt=0.1.

Attributes:
A

State matrix of the StateSpace system.

B

Input matrix of the StateSpace system.

C

Output matrix of the StateSpace system.

D

Feedthrough matrix of the StateSpace system.

dt

Return the sampling time of the system, None for lti systems.

poles

Poles of the system.

zeros

Zeros of the system.

Methods

__mul__(other)

Post-multiply another system or a scalar

to_ss()

Return a copy of the current StateSpace system.

to_tf(**kwargs)

Convert system representation to TransferFunction.

to_zpk(**kwargs)

Convert system representation to ZerosPolesGain.

See also

TransferFunction, ZerosPolesGain, lti, dlti
ss2zpk, ss2tf, zpk2sos

Notes

If the parameter system is a tuple (A, B, C, D) with four state space matrices, then those matrices are converted into two-dimensional arrays by calling abcd_normalize. Their dtypes will be “complex128” if any of the matrices are complex-valued. Otherwise, they will be of type “float64”.

Changing the value of properties that are not part of the StateSpace system representation (such as zeros or poles) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, call sys = sys.to_zpk() before accessing/changing the zeros, poles or gain.

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

StateSpace 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

>>> from scipy import signal
>>> import numpy as np
>>> a = np.array([[0, 1], [0, 0]])
>>> b = np.array([[0], [1]])
>>> c = np.array([[1, 0]])
>>> d = np.array([[0]])

>>> sys = signal.StateSpace(a, b, c, d)
>>> print(sys)
StateSpaceContinuous(
array([[0., 1.],
       [0., 0.]]),
array([[0.],
       [1.]]),
array([[1., 0.]]),
array([[0.]]),
dt: None
)

>>> sys.to_discrete(0.1)
StateSpaceDiscrete(
array([[1. , 0.1],
       [0. , 1. ]]),
array([[0.005],
       [0.1  ]]),
array([[1., 0.]]),
array([[0.]]),
dt: 0.1
)

>>> a = np.array([[1, 0.1], [0, 1]])
>>> b = np.array([[0.005], [0.1]])

>>> signal.StateSpace(a, b, c, d, dt=0.1)
StateSpaceDiscrete(
array([[1. , 0.1],
       [0. , 1. ]]),
array([[0.005],
       [0.1  ]]),
array([[1., 0.]]),
array([[0.]]),
dt: 0.1
)
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