MAE509 (LMIs in Control): Lecture 14, part A - The S-Procedure and Quadratic Stability using the LFT

all right hello class and uh welcome back to lecture 14. make sure our tablet's working all right so this is our third and well it's not the last we're going to see of robust control but it's the last lecture devoted perhaps exclusively to robust control i suppose i could say the the lectures on sos which follow

this also deal with the problem of robust control but uh also deal with non-linear stuff and so it's a sort of a mixed bag from from lecture 15 on so in this lecture we are going to have a quite a few we're going to introduce quite a few lmi's for robust control a fraction of course

of the lmi's that are out there so you can just look at um boyd's book on lmi's and systems and controls and you'll find many more but i think what we're going to cover today and we'll be covered in lecture 13 of course was was also a highlight what we covered today are the highlights

of lmi's for robust control lmis for robust control in the lft framework all right so we're going to be focusing on that lft framework and uh as i said well we'll mention this a bit uh going forward but uh the lft framework allows us to understand or to analyze systems where the uh the uncertainties don't enter quite

as neatly as they do in the in the additive the separable polytopic and interval uncertainty case which we considered in lecture 13. so well if this has i think you're gonna have two parts uh so the first part is going to consider the problem of unstructured uncertainty

in the lft framework and then starting with lecture slide 17 or something like that we'll consider the case of structured uncertainty