MAE509 (LMIs in Control): Lecture 14, part C - LMIs for Robust Control with Structured Uncertainty

all right class well welcome to the last part of this set of three lectures uh this is part b of lecture 14 i believe uh in uh well actually we had a part b uh so we broke part a down into two parts so technically i guess it's part c it's listed as part c but

really breaking this lecture down into two parts part a the first one through 16 slides which are unstructured uncertainty and in this set of slides we'll consider the case of structured uncertainty all right so i should add a d there structured norm bounded uncertainty in particular in lecture 13 we could of course

considered interval and polytopic uncertainty with sort of an additive structure and in this case in this lecture 14 we considered the lft and so draw an lft here delta which allows us to consider more general classes of uncertainty in particular we can do a polytopic uncertainty here but we're going to focus on the

the case of norm bounded uncertainty so we've got more bounded uncertainty here and in particular we'll consider uh the case of structured uncertainty so if you remember lecture 12 uh when we sort of derived these lft representations for several cases all of the cases that we derived had this structured uncertainty uh form right so

if we looked at broke down this uh this delta block what it uh represented if you recall there was like a delta m for our mass variability there was a delta c for our damper variability and there was a delta k for our spring variability right so and everything off diagonal was zero

right so that was our uncertainty and clearly this has a structure to it right so all of these there are a lot of zeros here and if we uh just do the unstructured uncertainty case we're going to get pretty conservative results because the unstructured results that we had on the part a of this lecture um well we'll