New conditions for the convergence of H∞ filters and predictors

The finite-horizon H_∞ filtering and prediction problems in the discrete-time case admit solutions only if a suitable difference Riccati equation is solved by a matrix sequence satisfying “feasibility” conditions. In this work, sufficient conditions ensuring the existence of filters and predictors over an arbitrarily long time interval are derived. Moreover, it is shown that, under these conditions, finite horizon estimators tend to stable stationary ones as the time horizon increases