Transient and Asymptotic Analysis of Discrete-Time H∞-Filters

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