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(s)=10(s+0.5)(s+10−6)(s+2−5i)(s+2+5i)

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

Control System Toolbox Documentation

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