# Documentation

## Creating Discrete-Time Models

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

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