Controllability for distributed nondiagonal bilinear systems

1. Distributed bilinear systems By a distributed bilinear system we mean a system of the form w(t) = Aw(t) + p(t)Bw(t), (1.1) w(0) = w0 ?? X, (1.2) where A generates a C0 semigroup of bounded linear operators exp(At) on a (possibly complex) Banach space X, B: X ?? X is a bounded linear operator, and p ?? L1([0,T];IR) is a real valued control defined on a specified interval [0,T].