ABSTRACT
The control system we deal with is described by the following nonlinear abstract differential equation (with initial condition):
y'(t) + Ay(t) + ft(y(t) - </>) 9 Bu(t) + f ( t ) , t € (0,T), 0(0) = 2/0-
We impose the following hypotheses on the data of equation (2.1): (HI) A : V -¥ V is a linear continuous and symmetric operator, where V is a real Hilbert space
continuously, densely and compactly embedded in H with V its dual space. (Identifying
n with its own dual, we have V C H C V.) Denoting by (•, •) the pairing between V and V', and by | • y the norm of V, we also assume that, for some u > 0 and a 6 E,
(Ay, y) + a|y|2 > u\y\2v for all y e V.
