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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 [R168], the generalized bilinear approximation is based on [R169] and [R170].

  References

  [R168] | (1, 2) http://en.wikipedia.org/wiki/Discretization#Discretization_of_linear_state_space_models

  [R169] | (1, 2) http://techteach.no/publications/discretetime_signals_systems/discrete.pdf

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