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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'

'AbsTol, RelTol'

Absolute and relative error tolerance for stable/unstable decomposition. Positive scalar values. When decomposing a model G, stabsep ensures that the frequency responses of G and GS + GU differ by no more than AbsTol + RelTol*abs(G). Increasing these tolerances helps separate nearby stable and unstable modes at the expense of accuracy. See stabsep for more information.

Default: AbsTol = 0; RelTol = 1e-8

'Offset'

Offset for the stable/unstable boundary. Positive scalar value. The first output of stabsepincludes 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.