package scipy

Discrete-time Linear Time Invariant system in state-space form.

Represents the system as the discrete-time difference equation :math:`xk+1 = A xk + B uk`. `StateSpace` systems inherit additional functionality from the `dlti` class.

Parameters ---------- *system: arguments The `StateSpace` class can be instantiated with 1 or 3 arguments. The following gives the number of input arguments and their interpretation:

* 1: `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 `True` (unspecified sampling time). Must be specified as a keyword argument, for example, ``dt=0.1``.

See Also -------- TransferFunction, ZerosPolesGain, 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.

Examples -------- >>> from scipy import signal

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

>>> 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 )

Calculate Bode magnitude and phase data of a discrete-time system.

Returns a 3-tuple containing arrays of frequencies rad/s, magnitude dB and phase deg. See `dbode` for details.

Examples -------- >>> from scipy import signal >>> import matplotlib.pyplot as plt

Transfer function: H(z) = 1 / (z^2 + 2z + 3) with sampling time 0.5s

>>> sys = signal.TransferFunction(1, 1, 2, 3, dt=0.5)

Equivalent: signal.dbode(sys)

>>> w, mag, phase = sys.bode()

>>> plt.figure() >>> plt.semilogx(w, mag) # Bode magnitude plot >>> plt.figure() >>> plt.semilogx(w, phase) # Bode phase plot >>> plt.show()

Calculate the frequency response of a discrete-time system.

Returns a 2-tuple containing arrays of frequencies rad/s and complex magnitude. See `dfreqresp` for details.

Return the impulse response of the discrete-time `dlti` system. See `dimpulse` for details.

Return the response of the discrete-time system to input `u`. See `dlsim` for details.

Return the step response of the discrete-time `dlti` system. See `dstep` for details.

Return a copy of the current `StateSpace` system.

Returns ------- sys : instance of `StateSpace` The current system (copy)

Convert system representation to `TransferFunction`.

Parameters ---------- kwargs : dict, optional Additional keywords passed to `ss2zpk`

Returns ------- sys : instance of `TransferFunction` Transfer function of the current system

Convert system representation to `ZerosPolesGain`.

Parameters ---------- kwargs : dict, optional Additional keywords passed to `ss2zpk`

Returns ------- sys : instance of `ZerosPolesGain` Zeros, poles, gain representation of the current system

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.