An Innovation Approach to<tex>$H_infty$</tex>Fixed-Lag Smoothing for Continuous Time-Varying Systems

Abstract

This note studies the finite horizon H/sub /spl infin// 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/sub /spl infin// 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/sub /spl infin// filtering RDE and one H/sub 2/ type of RDE. Examples demonstrate the proposed H/sub /spl infin// fixed-lag smoother design and the fact that the existence of an H/sub /spl infin// smoother does not depend on the solvability of H/sub /spl infin// filtering.