  From a theory developed by C. Mehl, et al., a theory of the rank one
perturbation of Hamiltonian systems with periodic coefficients is proposed. It
is showed that the rank one perturbation of the fundamental solution of
Hamiltonian system with periodic coefficients is solution of its rank one
perturbation. Some results on the consequences of the strong stability of these
types of systems on their rank one perturbation is proposed. Two numerical
examples are given to illustrate this theory.
