Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems

This paper studies the convergence and properties of the solutions of the Riccati difference equation. Special emphasis is given to systems which are not necessarily stabilizable (in the filtering sense), particularly those having uncontrollable roots on the unit circle. Besides generalizing and unifying previous work, the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components.