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 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
)

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.
den	Denominator of the TransferFunction system.
dt	Return the sampling time of the system, None for lti systems.
gain	Gain of the ZerosPolesGain system.
num	Numerator of the TransferFunction system.
poles	Poles of the system.
zeros	Zeros of the system.

Methods

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.