Linear Time Invariant system in state-space form.
Represents the system as the continuous-time, first order differential equation :math:`\dotx = A x + B u` or the discrete-time difference equation :math:`xk+1 = A xk + B uk`. `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 3 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``.
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.
Examples -------- >>> from scipy import signal
>>> 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 )