# Documentation

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# freqsepOptions

Options for slow-fast decomposition

## Syntax

``opt = freqsepOptions``
``opt = freqsepOptions(Name,Value)``

## Description

````opt = freqsepOptions` returns the default options for `freqsep`.```

example

````opt = freqsepOptions(Name,Value)` returns an options set with the options specified by one or more `Name,Value` pair arguments.```

## Examples

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Decompose a model into slow and fast components between poles that are closely spaced.

The following system includes a real pole and a complex pair of poles that are all close to s = -2.

`G = zpk(-.5,[-1.9999 -2+1e-4i -2-1e-4i],10);`

Try to decompose the model about 2 rad/s, so that the slow component cotains the real pole and the fast component contains the complex pair.

`[Gs,Gf] = freqsep(G,2);`
```Warning: One or more fast modes could not be separated from the slow modes. To force separation, increase the absolute or relative tolerances ("AbsTol" and "RelTol" options). Type "help freqsepOptions" for more information. ```

These poles are too close together for `freqsep` to separate. Increase the relative tolerance to allow the separation.

```options = freqsepOptions('RelTol',1e-4); [Gs,Gf] = freqsep(G,2,options);```

Now `freqsep` successfully separates the dynamics about 2 rad/s.

`slowpole = pole(Gs)`
```slowpole = -1.9999 ```
`fastpole = pole(Gf)`
```fastpole = -2.0000 + 0.0001i -2.0000 - 0.0001i ```

## Input Arguments

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### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside single quotes (`' '`). You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: `'AbsTol',1e-4`

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Absolute tolerance for slow-fast decomposition, specified as a nonnegative scalar value. `freqresp` ensures that the frequency responses of the original system, `G`, and the sum of the decomposed systems `Gs+Gf`, differ by no more than `AbsTol + RelTol*abs(G)`. Increase `AbsTol` to help separate nearby modes, at the expense of the accuracy of the decomposition.

Relative tolerance for slow-fast decomposition, specified as a nonnegative scalar value. `freqresp` ensures that the frequency responses of the original system, `G`, and the sum of the decomposed systems `Gs+Gf`, differ by no more than `AbsTol + RelTol*abs(G)`. Increase `RelTol` to help separate nearby modes, at the expense of the accuracy of the decomposition.

## Output Arguments

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Options for `freqsep`, returned as a `freqsepOptions` options set. Use `opt` as the last argument to `freqsep` when computing slow-fast decomposition.