Specifying Input/Output Delays :: LTI Models (Creating and Manipulating Models)

Creating and Manipulating Models

Specifying Input/Output Delays

Using the ioDelay property, you can specify frequency-domain models with independent delays in each entry of the transfer function. In continuous time, such models have a transfer function of the form

where the's are rational functions of , and is the time delay between input and output . See Specifying Delays in Discrete-Time Models for details on the discrete-time counterpart. We collectively refer to the scalars as the I/O delays.

The syntax to create above is

```
H = tf(num,den,'ioDelay',Tau)
```

```
H = zpk(z,p,k,'ioDelay',Tau)
```

where

num, den (respectively, z, p, k) specify the rational part of the transfer function
Tau is the matrix of time delays for each I/O pair. That is, Tau(i,j) specifies the I/O delay in seconds. Note that Tau and should have the same row and column dimensions.

You can also use the ioDelay property in conjunction with state-space models, as in

```
sys = ss(A,B,C,D,'ioDelay',Tau)
```

This creates the LTI model with the following transfer function.

Here is the entry of

Note State-space models with I/O delays have only a frequency-domain interpretation. They cannot, in general, be described by state-space equations with delayed inputs and outputs.

Functions that Support Time Delays Distillation Column Example