On the discrete-time H∞ filter via game theoretic approach

The authors consider discrete-time H_∞ filters based on a game-theoretic approach. The H_∞ filters are developed based on the discrete-time linear-quadratic (LQ) game. The authors obtain two different filters: a one-step predictor and a filter that yields the current state estimate. It is shown that the steady-state filters exist if an algebraic Riccati equation has a nonnegative solution and that both of the filters satisfy the H_∞ norm bound. The worst disturbance maximizing the energy ratio of the estimation error to the disturbance is also given by linear feedback of the estimation error. Furthermore, the authors propose an H_∞ fixed-lag smoother based on the H_∞ filter derived