On the optimal filtering problem of linear discrete-time periodic systems

Consideration is given to the periodic Riccati difference equation for the optimal filtering problem of linear periodic discrete-time systems. Specifically, a number of results are provided 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 analyzed. The results have been established under weaker assumptions and include both necessary and sufficient conditions.<>