White noise H∞H∞ fixed-lag smoothing for continuous time systems

The paper is to investigate the white noise fixed-lag smoothing problem in an H∞H∞ setting for continuous-time systems. Although H2H2 white noise fixed-lag smoothing and filtering have been well studied, the white noise smoothing under H∞H∞ index remains difficult since the latter is equivalent to a time delay problem. Actually, by introducing a Krein-space state space model, it will be shown that the H∞H∞ white noise central smoother is an H2H2 fixed-lag smoothing with delayed measurements. To overcome the time delay, the re-organized innovation analysis approach is adopted in this paper. The derived fixed-lag smoother is given in terms of two differential Riccati equations (DREs) with the same order as that of the original system.