Parametric solutions to the discrete periodic regul ator equations

Forward-time discrete periodic regulator matrix equations (FDPRE) and reverse-time discrete periodic regulator matrix equations (RDPRE) are firstly studied. The controllability and observability Gramians related with the lifting time variant system are utilized to constitute solutions. Parametric and explicit solutions to these two equations are presented in the form of iteration. The proposed method can provide sufficient design degree of freedom, since there are infinite solutions to be obtained. A detailed algorithm is also presented and its correctness is checked by a numerical example.