ABSTRACT
The feedbacks are unbounded and nonlinear. Various examples are displayed, which show that our framework is fairly general, even
if the results are not necessarily (all) new.
We begin with a well-known case in control theory, namely an elastic system with bounded damping on velocity
(1) utt + Au + C *C ut = 0 ( t> 0 ) ,
where A is a linear (unbounded) operator on a Hilbert space H, with domain D(A) dense in H,
self-adjoint, coercive, and with compact resolvent (I + \ A ) We assume the observation operator C e £(H,U), where U is another Hilbert space, and C* g jC(U,H) is the adjoint of C, so that the feedback operator C*C is linear bounded on H. This is an adequate framework for distributed feedback in the case of P.D.E.'s.
