AN OBSERVER FOR INFINITE-DIMENSIONAL DISSIPATIVE BILINEAR-SYSTEMS

We consider bilinear systems of the form x(t) = Ax(t) + u(t)Bx(t), y(t ) = [x(t),c] on an infinite-dimensional Hilbert space H, where A is th e generator of a semigroup of contraction, B is a bounded dissipative operator and c is-an-element-of H. The input signal u is-an-element-of L(infinity) (R+) such that u(t) greater-than-or-equal-to 0 for almost every t is-an-element-of R+. We present a simple observer for this cl ass of systems with the estimation error converging weakly to zero in H for every sufficiently rich input (inputs that we call ''regularly p ersistent''). Our result is a generalization of the previous results i n [1,2].