Please watch https://youtu.be/5x5hz81cgLs (NEW version in @ASalaControlEN channel).
This video outlines 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.
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''; the slides are correct, I just kind of abbreviate the speech but please pay attention to the correctly written esxpressions 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.
A Matlab case study is discussed in videos:
https://youtu.be/WIiduYRd-W8 , https://youtu.be/SZUnF2N6MYk ,
https://youtu.be/plRgjh8LnRU , https://youtu.be/ojGr5p_Z0q8 , https://youtu.be/1LNDDXw81FY .
__________
Further info and PDF at http://personales.upv.es/asala/YT/V/prth1EN.html
__________
Please subscribe to support the channel if you enjoy control engineering stuff, thanks!
Antonio Sala, UPV
