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Create option set for discrete- to continuous-time conversions


Use d2cOptions to specify the discretization method and associated quantities for discretizing models with d2c.



opts = d2cOptions returns the default options for d2c.


opts = d2cOptions(Name=Value) creates an option set with the options specified by one or more name-value arguments.


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Discrete-to-continuous time conversion method, specified as one of the following values:

'zoh'Zero-order hold, where d2c assumes that the control inputs are piecewise constant over the sample time Ts.

Linear interpolation of the inputs (modified first-order hold). Assumes that the control inputs are piecewise linear over the sampling period.

'tustin'Bilinear (Tustin) approximation. By default, d2c converts with no prewarp. To include prewarp, use the PrewarpFrequency option.
'matched'Zero-pole matching method. (See [1], p. 224.)

For information about the algorithms for each d2c conversion method, see Continuous-Discrete Conversion Methods.

Prewarp frequency for 'tustin' method, specified in rad/TimeUnit, where TimeUnit is the time units, specified in the TimeUnit property, of the discrete-time system. Specify the prewarp frequency as a positive scalar value. A value of 0 corresponds to the 'tustin' method without prewarp.

Since R2024a

Option to specify state and delay consistency in state-space arrays, specified as 'off' or 'on'.

  • 'on' — Provide state and delay consistency across the resulting array of state-space models.

  • 'off' — Allow additional states when encountering poles a z = 0.


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Consider the following discrete-time transfer function.


Create the discrete-time transfer function with a sample time of 0.1 seconds.

Hd = tf([1 1],[1 1 1],0.1);

Specify the discretization method as bilinear (Tustin) approximation and the prewarp frequency as 20 rad/seconds.

opts = d2cOptions('Method','tustin','PrewarpFrequency',20);

Convert the discrete-time model to continuous-time using the specified discretization method.

Hc = d2c(Hd,opts);

You can use the discretization option set opts to discretize additional models using the same options.


[1] Franklin, G.F., Powell,D.J., and Workman, M.L., Digital Control of Dynamic Systems (3rd Edition), Prentice Hall, 1997.

Version History

Introduced in R2012a

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See Also