scipy.signal.cont2discrete(sys, dt, method='zoh', alpha=None)[source]

Transform a continuous to a discrete state-space system.


sys : a tuple describing the system.

The following gives the number of elements in the tuple and the interpretation:

  • 2: (num, den)
  • 3: (zeros, poles, gain)
  • 4: (A, B, C, D)

dt : float

The discretization time step.

method : {“gbt”, “bilinear”, “euler”, “backward_diff”, “zoh”}, optional

Which method to use:

  • gbt: generalized bilinear transformation
  • bilinear: Tustin’s approximation (“gbt” with alpha=0.5)
  • euler: Euler (or forward differencing) method (“gbt” with alpha=0)
  • backward_diff: Backwards differencing (“gbt” with alpha=1.0)
  • zoh: zero-order hold (default)

alpha : float within [0, 1], optional

The generalized bilinear transformation weighting parameter, which should only be specified with method=”gbt”, and is ignored otherwise


sysd : tuple containing the discrete system

Based on the input type, the output will be of the form

  • (num, den, dt) for transfer function input
  • (zeros, poles, gain, dt) for zeros-poles-gain input
  • (A, B, C, D, dt) for state-space system input


By default, the routine uses a Zero-Order Hold (zoh) method to perform the transformation. Alternatively, a generalized bilinear transformation may be used, which includes the common Tustin’s bilinear approximation, an Euler’s method technique, or a backwards differencing technique.

The Zero-Order Hold (zoh) method is based on [R168], the generalized bilinear approximation is based on [R169] and [R170].


[R168](1, 2)
[R169](1, 2)
[R170](1, 2) G. Zhang, X. Chen, and T. Chen, Digital redesign via the generalized bilinear transformation, Int. J. Control, vol. 82, no. 4, pp. 741-754, 2009. (

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