How to ensure existence and convergence of the discrete-time finite-horizon H∞ filter

It is known that the discrete-time H_∞ finite-horizon filter exists provided that the solution of a suitable H_∞ Difference Riccati Equation (DRE) exists and satisfies a "feasibility" condition. In the paper, sufficient conditions ensuring feasibility and convergence to the steady-state stabilizing solution are derived. In particular, convergence can be guaranteed if the initial condition of the DRE is not much greater than the stabilizing solution. For a fixed value of the attenuation level γ, the finite-horizon H_∞-filter may fail to converge to the steady-state stabilizing filter. Hence, a strategy employing a time varying attenuation level γ(t) is worked out so as to ensure both feasibility and convergence to the desired steady-state filter.