  The concept of (A,B)-invariant subspace (or controlled invariant) of a linear
dynamical system is extended to linear systems over the max-plus semiring.
Although this extension presents several difficulties, which are similar to
those encountered in the same kind of extension to linear dynamical systems
over rings, it appears capable of providing solutions to many control problems
like in the cases of linear systems over fields or rings. Sufficient conditions
are given for computing the maximal (A,B)-invariant subspace contained in a
given space and the existence of linear state feedbacks is discussed. An
application to the study of transportation networks which evolve according to a
timetable is considered.
