H∞ Fixed-lag smoothing for discrete linear time-varying systems

This paper is concerned with the finite horizon H∞ fixed-lag smoothing problem for discrete linear time-varying systems. The existence of an H∞ smoother is first related to certain inertia condition of an innovation matrix. The innovation matrix is traditionally computed via a Riccati difference equation (RDE) associated with the H∞ filtering of an augmented system which is computationally expensive. To avoid solving the RDE of high dimension, we introduce a re-organized innovation and apply innovation analysis and projection theory in Krein space to give a simple method of computing the innovation matrix. The H∞ smoother is computed as a projection in Krein space by performing two RDEs of the same dimension as that of the original system.