H/sup (infinity)/ control and estimation with preview-part II: fixed-size ARE solutions in discrete time

H/sup (infinity)/ preview control and fixed-lag smoothing problems are solved in general discrete time linear systems, via a reduction to equivalent open-loop differential games. To prevent high order Riccati equations, found in some solutions, the state of the Hamilton-Jacobi system resides in a quotient space of an auxiliary extended state space system. The dimension of that auxiliary space is equal to the state space dimension of the original system (ignoring the delay).