  In this paper it is considered a class of infinite-dimensional control
systems in a variational setting. By using a Faedo-Galerkin method, a sequence
of approximating finite dimensional controlled differential equations is
defined. On each of these systems a variable structure control is applied to
constrain the motion on a specified surface. Under some growth assumptions the
convergence of these approximations to an ideal sliding state for the
infinite-dimensional system is shown. Results are then applied to the Neumann
boundary control of a parabolic evolution equation.
