An observer for infinite-dimensional dissipative bilinear systems

We consider bilinear systems of the form , y(t)= χ(t),c on an infinite-dimensional Hilbert space H, where A is the generator of a semigroup of contraction, B is a bounded dissipative operator and c H. The input signal u L∞ (R+) such that u(t) 0 for almost every t R+. We present a simple observer for this class of systems with the estimation error converging weakly to zero in H for every sufficiently rich input (inputs that we call “regularly persistent”). Our result is a generalization of the previous results in [1,2].