Structured Robust Stability

qWe are interested in the following question: How large *D* (in the sense of ||*D*||¥) can be without
destabilizing the feedback system?

Since the closed-loop poles are
given by det(*I-G(s)**D*)=0 the feedback system becomes
unstable if det(*I-G*(*s*)*D*(*s*))=0
for some s in the closed right half plane. Now
let a>0 be a sufficiently small number such that the
closed-loop system is stable for all stable ||*D*||¥< a. Next increase a until amax so that the closed-loop system becomes unstable. So amax is the **robust stability margin**.

qConsider a general feedback interconnection where *D** *is structured uncertainty block and *G*(*s*) is the interconnection
matrix.