Why do I receive unexpected results for stability using the ROBUSTSTAB command in Robust Control Toolbox?

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MathWorks Support Team 2009-6-27

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I have an unstable system containing only parameter uncertainty (ureal). However, using the ROBUSTSTAB command indicates that my system is stable.

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Answer 1

MathWorks Support Team 2009-6-27

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This enhancement has been incorporated in Release 2008a (R2008a).

For previous product releases, read below for any possible workarounds:

To estimate the robust stability margin over an entire frequency range, the function ROBUSTSTAB performs this basic computation for a finite set of frequencies and looks at the worst case over this set.

However, in some problems with only parameter uncertainty (ureal), the migration of poles from stable to unstable can occur at isolated frequencies. As a result, any frequency grid that excludes these particular frequencies fails to detect worst-case perturbations and give over-optimistic stability margins.

The Robust Control Toolbox demo titled "Getting Reliable Estimates of Robustness Margins" in the online documentation describes how to circumvent this issue.