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

Abstract

It is known that the finite-horizon H ∞ -filter exists provided that the solution of a suitable H ∞ Difference 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 ofthe DRE is not much greater than the stabilising solution. For a fixed value of the attenuation level γ the finite-horizon H ∞ -filter may fail to converge to the steady-state stabilising 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.