Parametrization of Discrete-Time H_∞ Filters Based on Model Matching

Abstract

This paper is concerned with a state-space solution to the H_∞ filtering problem for linear discrete-time systems. We first reduce the H_∞ filtering problem to a model matching problem (MMP), and then employ a (J, J')-spectral factorization technique for solving the MMP. By this approach, we obtain a complete parametrization of all H_∞ filters. Using the chain scattering representation, the structure of the H_∞ filtering problem is also studied. Furthermore, we present a solution to the H_∞ prediction problem as a special case of the filtering problem.