How is it guaranteed that ROBSTAB finds the worst-case stability margin over the complete frequency range without gridding?

How is it guaranteed that ROBSTAB finds the worst-case stability margin over the complete frequency range without grinding? Can you provide the principle of the underlying algorithm/method or a source? Can you also provide information on which approach is used to calculate the lower and upper bound on Mu?

Answer 1

[MathWorks Support Team]

Before MATLAB R2016b, Mu calculations were done on frequency grids. While it was fine for complex uncertainty, this was prone to miss peaks and discontinuities in the presence of uncertain real parameters, often leading to over-optimistic stability margins.

Starting in MATLAB R2016b, functions like ROBSTAB, ROBGAIN, and WCGAIN use a modified algorithm that eliminates this issue. The main change is in the Mu upper bound computation, which seeks to certify entire intervals rather than just individual frequencies and to cover the entire frequency axis with such interval certificates. This is how we obtain a guarantee over the entire frequency range.