Abstract
This paper considers the discrete-time H∞ filters derived by game theoretic approach. We obtain two different filters, namely one-step predictor and filter that yields the current state estimate, according to the available information for the linear-quadratic game. We show that the steady-state filters exist if an algebraic Riccati equation has a nonnegative solution and that both of the filters satisfy H∞-norm bound based on spectral factorization. The worst disturbance maximizing the energy ratio of the estimation error to the disturbance is also given by a linear feedback of the estimation error. Furthermore, we propose an H∞ fixed-lag smoother based on the H∞ filter derived here. Simulation results are included to show the difference between H2 and H∞ filters.
