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

摘要

The paper is to investigate the white noise fixed-lag smoothing problem in an H_∞ setting for continuous-time systems. Although H_2 white noise fixed-lag smoothing and filtering have been well studied, the white noise smoothing under 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_∞ white noise central smoother is an H_2 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.