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rho - frequency-wise stability margin

version 1.1 (4.53 KB) by

Frequency-wise stability margin for a [P,C] pair



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rho calculates the frequency-wise stability margin for a plant-controller pair. This gives the user the ability to understand how the closed-loop robustness varies according to frequency.

This function provides functionality that is not in Control System Toolbox or Robust Control Toolbox. It is compatible with both products.


[r,rinf,omega] = rho(P,C) or [r,rinf] = rho(P,C,omega) returns the frequency-wise stability margin for the plant-controller pair [P,C] as defined in Vinnicombe (2000, p.68). This essentially gives a frequency-wise measure of the plant-controller pair's robustness. rinf is the infimum of r, unless [P,C] is unstable in which case it is set to zero and a warning message is generated.
rho(P,C) or rho(P,C,omega) without any output arguments will display the results in graphical form.
1. Vinnicombe, G. (2000) Uncertainty and Feedback: H-Infinity Loop-Shaping and the v-Gap Metric. London: Imperial College
See also: sigma

Comments and Ratings (1)

Daniel Auger

There's a bug in the stability test (incorrect sign convention) in the version uploaded on 13 Feb 2013. A corrected version has been submitted for upload.



Fixed a bug: sign convention of feedback stability test was wrong. Also clarified sign convention. Altered test scripts to make the sign convention clearer.

MATLAB Release
MATLAB 8.0 (R2012b)
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