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.
