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scipy.signal.

# StateSpace

class scipy.signal.StateSpace(*system, **kwargs)

  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:

      > - 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`)

      > - 4: array_like: (A, B, C, D)

    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

  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.

  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
      )