Stability conditions for linear periodic Hamiltonian systems

In this paper we give sufficient conditions for stability of a linear system described by a set of differential equations of the form Xi = ??j=1 2k hk+i,j(t)Xj, i = 1,...., k (1) Xk+i = - ??j=1 2k hi,j(t)Xj, i = 1,..., k where each coefficient hij(t) is periodic of period T > 0 and Lebesque integrable on [0, T]. We also assume that hij(t) = hji(t), i, j = 1..., 2k.