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.

Notes

Changing the value of properties that are not part of the StateSpace system representation (such as zeros or :None:None:`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.

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:None:`None` (continuous-time). Must be specified as a keyword argument, for example, dt=0.1 .

Linear Time Invariant system in state-space form.

See Also

TransferFunction

ZerosPolesGain

dlti

lti

ss2tf

ss2zpk

zpk2sos

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
)

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._ltisys.dlti scipy.signal._ltisys.ZerosPolesGain.to_ss scipy.signal._ltisys.StateSpaceDiscrete scipy.signal._ltisys.LinearTimeInvariant._as_ss scipy.signal._ltisys.TransferFunctionContinuous scipy.signal._ltisys.StateSpace scipy.signal._ltisys.lti scipy.signal._ltisys.StateSpace.to_ss scipy.signal._ltisys.TransferFunction scipy.signal._ltisys.dlsim scipy.signal._ltisys.TransferFunctionDiscrete scipy.signal._ltisys.TransferFunction.to_ss scipy.signal._ltisys.StateSpace.__repr__ scipy.signal._ltisys.StateSpaceContinuous scipy.signal._ltisys.StateSpaceContinuous.to_discrete scipy.signal._ltisys.TransferFunction._copy scipy.signal._ltisys.StateSpace._copy scipy.signal._ltisys.ZerosPolesGainDiscrete scipy.signal._ltisys.ZerosPolesGainContinuous scipy.signal._ltisys.ZerosPolesGain

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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