Normalised factorisation uncertainty: nu-gap metric geometric interpretation, general case (no proofs)

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 11:35

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Summary:

This video extends the discussion of the videos [gapm1EN] and [gapm1bEN], which reviewed the geometric interpretation of the $\nu$-gap in the real case. Here, the notions are generalized to the complex case of $\nu$-gap distance between $P_1(j\omega )\in ℂ$ and $P_2(j\omega )\in ℂ$, also interpretable in the SISO case as chordal distance in stereographic projection. Transfer matrix formulae for MIMO cases are stated without proof, and briefly commented upon. Matlab’s gapmetric command is related to the ideas and computations here described.

The usefulness of all this lies in the fact that, given a controller $K$, if the $\nu$-gap between $P_1$ and $P_2$ is smaller than the normalised coprime factorisation robustness margin (ncfmargin) of the loop $P_1$, $K$ then $P_2$ will be robustly stabilised by $K$.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.