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# stabsepOptions

Options for stable-unstable decomposition

## Syntax

```opts = stabsepOptions opts = stabsepOptions('OptionName', OptionValue) ```

## Description

`opts = stabsepOptions` returns the default options for the `stabsep` command.

`opts = stabsepOptions('OptionName', OptionValue)` accepts one or more comma-separated name/value pairs. Specify `OptionName` inside single quotes.

## Input Arguments

### Name-Value Pair Arguments

`'Focus'`

Focus of decomposition. Specified as one of the following values:

 `'stable'` First output of `stabsep` contains only stable dynamics. `'unstable'` First output of `stabsep` contains only unstable dynamics.

Default: `'stable'`

`'SepTol'`

Accuracy loss factor for stable/unstable decomposition. Positive scalar values. When decomposing a model G(s), `stabsep` ensures that the frequency responses of G and G1 + G2 differ by no more than `SepTol` times the absolute accuracy of the computed value of `G(s)`. Increasing `SepTol` helps separate nearby stable and unstable modes at the expense of accuracy.

Default: `10`

`'Offset'`

Offset for the stable/unstable boundary. Positive scalar value. The first output of `stabsep`includes only poles satisfying:

Continuous time:

• ```Re(s) < -Offset * max(1,|Im(s)|) (Focus = 'stable')```

• ```Re(s) > Offset * max(1,|Im(s)|) (Focus = 'unstable')```

Discrete time:

• `|z| < 1 - Offset` (```Focus = 'stable'```)

• `|z| >1 + Offset` (```Focus = 'unstable'```)

Increase the value of `Offset` to treat poles close to the stability boundary as unstable.

Default: `0`

For additional information on the options and how to use them, see the `stabsep` reference page.

## Examples

Compute the stable/unstable decomposition of the system given by:

`$G\left(s\right)=\frac{10\left(s+0.5\right)}{\left(s+{10}^{-6}\right)\left(s+2-5i\right)\left(s+2+5i\right)}$`

Use the `Offset` option to force `stabsep` to exclude the pole at s = 10–6 from the stable term of the stable/unstable decomposition.

```G = zpk(-.5,[-1e-6 -2+5i -2-5i],10); opts = stabsepOptions('Offset',.001); % Create option set [G1,G2] = stabsep(G,opts) % treats -1e-6 as unstable```

These commands return the result:

```Zero/pole/gain: -0.17241 (s-54) --------------- (s^2 + 4s + 29) Zero/pole/gain: 0.17241 ---------- (s+1e-006)```
The pole at s = 10–6 is in the second (unstable) output.

## See Also

Introduced in R2010a

## Support

#### Learn how to automatically tune PID controller gains

Download code examples