Analysis of the discrete-time periodic Riccati equation by a Kleinman procedure

In this paper, the problem of finding the symmetric and positive semidefinite periodic solutions of the discrete-time Riccati equation with periodic coefficients is considered. The solution can be seen as the limit of a sequence of periodic matrices obtained by solving a sequence of suitable periodic Lyapunov equations. The procedure is the discrete-time periodic version of the Kleinman technique. It also provides an existence sufficient condition on the grounds of which two necessary and sufficient conditions for the existence and uniqueness of the periodic solution are derived.