## Documentation |

This example shows how to create discrete-time linear models using the `tf`, `zpk`, `ss`, and `frd` commands.

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**Specifying Discrete-Time Models**

Control System Toolbox™ lets you create both continuous-time and discrete-time models. The syntax for creating discrete-time models is similar to that for continuous-time models, except that you must also provide a sample time (sampling interval in seconds).

For example, to specify the discrete-time transfer function:

with sampling period `Ts = 0.1 s`, type:

num = [ 1 -1 ]; den = [ 1 -1.85 0.9 ]; H = tf(num,den,0.1)

H = z - 1 ------------------ z^2 - 1.85 z + 0.9 Sample time: 0.1 seconds Discrete-time transfer function.

or equivalently:

```
z = tf('z',0.1);
H = (z - 1) / (z^2 - 1.85*z + 0.9);
```

Similarly, to specify the discrete-time state-space model:

with sampling period `Ts = 0.1 s`, type:

sys = ss(.5,1,.2,0,0.1);

**Recognizing Discrete-Time Systems**

There are several ways to determine if your LTI model is discrete:

The display shows a nonzero sample time value

`sys.Ts`or`get(sys,'Ts')`return a nonzero sample time value.`isdt(sys)`returns true.

For example, for the transfer function `H` specified above,

H.Ts

ans = 0.1000

isdt(H)

ans = 1

You can also spot discrete-time systems by looking for the following traits:

Time response plots - Response curve has a staircase look owing to its sampled-data nature

Bode plots - There is a vertical bar marking the Nyquist frequency (pi divided by the sample time).

The following plots show these characteristic traits:

step(H)

bode(H), grid

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