# Documentation

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# d2cOptions

Create option set for discrete- to continuous-time conversions

## Syntax

`opts = d2cOptionsopts = d2cOptions(Name,Value)`

## Description

`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` pair arguments.

## Input Arguments

### Name-Value Pair Arguments

`'method'`

Discretization method, specified as one of the following values:

 `'zoh'` Zero-order hold, where `d2c` assumes the control inputs are piecewise constant over the sample time `Ts`. `'foh'` Linear interpolation of the inputs (modified first-order hold). Assumes 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.)

Default: `'zoh'`

`'PrewarpFrequency'`

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.

Default: 0

## Examples

Convert a discrete-time model to continuous-time using the `'tustin'` method with frequency prewarping.

Create the discrete-time transfer function

`$\frac{z+1}{{z}^{2}+z+1}$`

`hd = tf([1 1], [1 1 1], 0.1); % 0.1s sample time`
To convert to continuous-time, use `d2cOptions` to create the option set.

```opts = d2cOptions('Method', 'tustin', 'PrewarpFrequency', 20); hc = d2c(hd, opts);```

You can use `opts` to resample additional models using the same options.

## References

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