Periodic Riccati difference equations: approaching equilibria by implicit systems

A parameterization of solutions to the periodic Riccati difference equation (RDE) is given. By using behavioral tools the moving equilibria of the periodic RDE are encompassed among the trajectories of the implicit AR model associated to the symplectic pencil of the corresponding Hamiltonian equations. This allows a parameterization of solutions of periodic RDEs even in the case the dynamic matrix is singular.