rho - frequency-wise stability margin

version (4.53 KB) by Daniel J. Auger
Frequency-wise stability margin for a [P,C] pair


Updated 14 Feb 2013

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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

Cite As

Daniel J. Auger (2022). rho - frequency-wise stability margin (https://www.mathworks.com/matlabcentral/fileexchange/40306-rho-frequency-wise-stability-margin), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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