Lyapunov inequalities of linear Hamiltonian systems on time scales

In this paper, we establish several Lyapunov-type inequalities for the following linear Hamiltonian systems x(Delta)(t) = -A(t)x(sigma(t)) - B(t)y(t), y(Delta)(t) = C(t)x(sigma(t)) + A(T)(t)y(t) on the time scale interval [a, b](T), [a, b] boolean AND T for some a, b is an element of T, where B and C are real n x n symmetric matrix-valued functions on [a, b](T) with B being semi-positive definite, A is real n x n matrix-valued function on [a, b](T) with I + mu(t)A being invertible, and x, y are real vector-valued functions on [a, b](T).