In this note it is shown that the main result of [1], concerning a characterization of a pair of structural invariant subspaces associated with the extended symplectic system, is a particular case of a result presented in [2] and [3] within a more general and rigorous context. We also analyse the proof of the main result of [1], and the way such result is used to accomodate the boundary conditions in the solution of a finite-horizon linear quadratic optimal control problem.