A reduction technique for generalised Riccati difference equations arising in linear-quadratic optimal

In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency index of the closed-loop, from another part that can be computed by iterating a reduced-order Riccati difference equation.