  It is well-known that the controllability of finite-dimensional nonlinear
systems can be established by showing the controllability of the linearized
system. However, this classical result does not generalize to
infinite-dimensional nonlinear systems. In this paper, we restrict ourselves to
semilinear infinite-dimensional systems, and show that the exact
controllability of the linearized system implies exact controllability of the
nonlinear system. The restrictions concerning the nonlinear operator are
similar to those that can be found in the literature about the linearized
stability analysis of semilinear systems.
