Robust performance: small-gain sufficient condition (h-infinity norm bound)

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 10:59

Summary:

This video presents the main “small gain” condition to ensure robust performance, the fact that the infinity norm of a given generalised plant $P$ is less than one is a sufficient condition for robust performance (under some scalings and assumptions).

The video proves the above assertion and also relates it with the small gain conditions for robust stability and nominal performance (arising, in both cases, from a “fragment” of $P$).

Erratum: in audio, I often say“less than” ($<$) but slides write “lower or equal than” ($\le$); the slides are correct, I just kind of abbreviate the speech but just pay attention to the correctly written expressions in the slides. Likewise, I say “negative” instead of “non-positive”; excuse my imprecise speech.

This condition will be further relaxed in forthcoming videos addressing the “scaled small gain” modification, and it will give rise to H-infinity control synthesis methods for robust performance (with so-called ”multipliers” or ”scalings”) conforming the basis of the mu-synthesis techniques.

A robust performance Matlab case study appears in videos [cerp1EN], [cerp2EN], [cerp3EN].

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