ABSTRACT
T heorem 3.1 Let W i(-))W 2(·) and P(-) be given as in the beginning of this section and define the corresponding Pritchard-Sal am on system E g as in (3 .3 ) . Furthermore, suppose that (t(Ao) f l ilR = 0 and let 7 > 0 . Then there exists a stabilizing (Pritchard-Salamon) controller E # such that
n 0 ^ x o a - p i w ) ) - 1
W 2(-)K(-)(I - P ( ' )K ( · ) ) - ' < 7,Ho i f and only i f there exist nonnegative definite operators P E £(V, V;) and Q E £(W ', W ) satisfying items (z),(n) and (Hi) of Theorem 2.3. Furthermore, in this case, one such controller is given by (2.23)-(2.24).
