An innovation approach to H∞ fixed-lag smoothing for continuous time-varying systems

This note studies the finite horizon H_∞ fixed-lag smoothing problem for linear continuous time-varying systems. A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H_∞ fixed-lag smoother. The condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two Riccati differential equations (RDEs), one standard H_∞ filtering RDE and one H₂ type of RDE. Examples demonstrate the proposed H_∞ fixed-lag smoother design and the fact that the existence of an H_∞ smoother does not depend on the solvability of H_∞ filtering.