This is a short report of the lecture on Tuesday 19 March.
We first briefly summarized the SISO RS and RP-conditions.
We then went on to the more general approach in Chapter 8.
1. Discussed why RS could be tested using M-Delta structure.
2. Derived M for a couple of cases.
3. Delta full matrix:
Derived RS-condition |M|<1 and its MIMO generalization
smax(M) < 1 (Sufficiency is obvious from small gain theorem,
necessaity follows since any phase in Delta is allowed and any
direction in Delta is allowed).
4. More generally for concex set of perturbations:
For real/complex Delta: RS iff det(I - M Delta) neq 0, forall Delta, forall freq.
For complex Delta: RS iff rho(M Delta) <1 forall freq.
4. Delta block diagonal: By definition of mu: RS iff mu(M)<1
5. Derived upper bound smax(D M D^-1) on mu(M) by
i. Noting that rho(M Delta) = rho(D M D^{-1} Delta) when
D is such that D \Delta D^-1 = Delta
ii. By using the idea of scaling in the M Delta block diagram
as in the book.
6. Showed that H-infinity robust performance (RP) is a special case of
RS by using the "block-diagram" proof in the book.
Best regards,
Sigurd
PS. The book is now ready for proof reading.