Periodic strong solution for the optimal filtering problem of linear discrete-time periodic systems

The periodic Riccati difference equation (PRDE) for the optimal filtering problem of linear periodic discrete-time systems is addressed. Specifically, the author provides a number of results on the existence, uniqueness, and stability properties of symmetric periodic nonnegative-definite solutions of the periodic Riccati difference equation in the case of nonreversible and nonstabilizable periodic systems. The convergence of symmetric periodic nonnegative-definite solutions of the periodic Riccati difference equation is also analyzed. The results have been established under weaker assumptions and include both necessary and sufficient conditions. The existence and properties of symmetric periodic nonnegative-definite solutions of the PRDE are established directly from the PRDE