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# scipy.signal.cont2discrete

`scipy.signal.``cont2discrete`(sys, dt, method='zoh', alpha=None)

  Transform a continuous to a discrete state-space system.

  Parameters:

  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

  Returns:

  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

  Notes

  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 [R176], the generalized bilinear approximation is based on [R177] and [R178].

  References

  [R176] | (1, 2) http://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models

  [R177] | (1, 2) http://techteach.no/publications/discretetime_signals_systems/discrete.pdf

  [R178] | (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. (http://www.ece.ualberta.ca/~gfzhang/research/ZCC07_preprint.pdf)