# pade

Padé approximation of models with time delay

## Description

`pade`

approximates time delays for continuous-time LTI models.
Such approximations are useful to model time delay effects such as transport and computation
delays within the context of continuous-time systems. The Laplace transform of a time delay of
*T* seconds is exp(–*sT*). This exponential transfer
function is approximated by a rational transfer function using the Padé approximation formulas
from [1].

To approximate discrete-time models, use `absorbDelay`

.

See Time Delays in Linear Systems for more information about models with time delays.

specifies independent approximation orders for each input, output, and I/O or internal delay
using vectors `sysx`

= pade(`sys`

,`NU`

,`NY`

,`NINT`

)`NU`

, `NY`

, and `NINT`

,
respectively. You can use scalar values for `NU`

, `NY`

, or
`NINT`

to specify a uniform approximation order. You can also set some
entries of `NU`

, `NY`

, or `NINT`

to
`Inf`

to prevent approximation of the corresponding delays.

## Examples

## Input Arguments

## Output Arguments

## Limitations

Padé approximation is valid only at low frequencies and provides better frequency-domain approximation than time-domain approximation. Therefore, compare the true and approximate responses to choose the right approximation order and check the approximation validity.

High-order Padé approximations produce transfer functions with clustered poles. Because such pole configurations tend to be very sensitive to perturbations, avoid Padé approximations with order

`N>10`

.

## References

[1] Golub, Gene H., and Charles F. Van Loan. Matrix Computations. 2nd ed. Johns Hopkins Series in the Mathematical Sciences 3. Baltimore, Md: Johns Hopkins University Press, 1989. pp. 557-558.

## Version History

**Introduced before R2006a**

## See Also

`c2d`

| `absorbDelay`

| `thiran`

| `delay2z`