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

This note studies the finite horizon H(infinity) fixed-lag smoothing problem for linear continuous time-varying systems. A new technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H(infinity) 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(infinity) filtering RDE and one H(2) type of RDE. Examples demonstrate the proposed H(infinity) fixed-lag smoother design and the fact that the existence of an H(infinity) smoother does not depend on the solvability of H(infinity) filtering.