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 \(x[k+1] = A x[k] + B u[k]\).
StateSpacesystems inherit additional functionality from thelti, respectively thedlticlasses, depending on which system representation is used.- Parameters:
- *system: arguments
The
StateSpaceclass can be instantiated with 1 or 4 arguments. The following gives the number of input arguments and their interpretation:1:
ltiordltisystem: (StateSpace,TransferFunctionorZerosPolesGain)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:
AState matrix of the
StateSpacesystem.BInput matrix of the
StateSpacesystem.COutput matrix of the
StateSpacesystem.DFeedthrough matrix of the
StateSpacesystem.dtReturn the sampling time of the system, None for
ltisystems.polesPoles of the system.
zerosZeros of the system.
Methods
__mul__(other)Post-multiply another system or a scalar
to_ss()Return a copy of the current
StateSpacesystem.to_tf(**kwargs)Convert system representation to
TransferFunction.to_zpk(**kwargs)Convert system representation to
ZerosPolesGain.See also
Notes
Changing the value of properties that are not part of the
StateSpacesystem representation (such aszerosorpoles) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, callsys = sys.to_zpk()before accessing/changing the zeros, poles or gain.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 )