The Stability Radius

Abstract

In Chapters 8 and 9, the stability of polynomial families

$$ P\left( {s,Q} \right)\; = \;\left\{ {p\left( {s,q} \right)\;|\;q\; \in \;Q} \right\}$$

(1)

with p(s, q) = ao(4) + ai(4)s +… + an(q)sn and q, E [4,; 4:], i = 1, 2,…, € was investigated. The primary interest was necessary and sufficient conditions for stability. These conditions give primarily a yes or no answer to the robust stability problem. If the answer is yes, then there is some kind of stability margin of the uncertain parameters, the domain Q of the parameters can be enlarged without loosing stability. The next question is: what is the smallest perturbation in the parameters q that destabilizes the system?