BACK TO THE ROBUST PERFORMANCE PROBLEM

The Main Loop Theorem is introduced in the particular context of a robust performance problem. Note that this Theorem has been widely

used in many other contexts, and that it is the basis of many existing // results.

4.4.1

BACK TO THE ROBUST PERFORMANCE PROBLEM

MAIN LOOP THEOREM

The standard interconnection structure M — A of Figure 1.11 is here again considered. The mixed model perturbation Д is split into two mixed model perturbations Д i and Д2:

Подпись:BACK TO THE ROBUST PERFORMANCE PROBLEM

Подпись: so that the standard interconnection structure Д — Д of Figure 1.11 can be equivalently rewritten as the interconnection structure of Figure 1.12. The complex matrix M is partitioned compatibly with equation (1.38) as:

(1.38)

BACK TO THE ROBUST PERFORMANCE PROBLEM

Let Д і = 0 and Fi( M, Д2) the transfer between w and z on Figure 1.13. The following result is known as the Main Loop Theorem: