Controllability for Distributed Bilinear Systems

This paper studies controllability of systems of the form dw / dt = Aw + p(t)Bw where A is the infinitesimal generator of a C⁰ semigroup of bounded linear operators eAt on a Banach space X, B:X → X is a C¹ map, and p ∈ L¹ ([0,T];R) is a control. The paper (i) gives conditions for elements of X to be accessible from a given initial state w₀ and (ii) shows that controllability to a full neighborhood in X of w₀ is impossible for X = ∞. Examples of hyperbolic partial differential equations are provided.