A unified approach to linear estimation for discrete-time systems. II. H∞ estimation

This paper focuses on developing a unified state-space approach to the H_∞ filtering, multistep prediction and fixed-lag smoothing. It is shown that the H_∞ estimation is in fact an H₂ estimation for an associated system with current and delayed measurements in Krein space. A necessary and sufficient condition for the existence of an H_∞ estimator is therefore derived using an innovation analysis method together with projection in Krein space. More importantly, the approach leads to a solution for the long standing H_∞ fixed-lag smoothing problem. Our approach does not require augmenting the state of the system and is similar to the forward and backward procedure in the H₂ fixed-lag smoothing. The H_∞ steady state estimation is also solved in terms of a Riccati equation of the same dimension as the system state