Continuous-time fixed-lag smoothing in an H∞ setting

In this paper, the effect of the smoothing lag h on the achievable performance level γ in continuous-time H^∞ fixed-lag smoothing is studied. It is shown that γ, in a sense, decays exponentially with h and, moreover, the decay ratio is completely determined by the dynamics of the corresponding Kalman filter, much like for H² smoothing, yet is is also shown that there exists a remarkable difference between the H² and H^∞ cases: whereas in the former case the performance improves monotonically with h, in the latter case the achievable γ typically "saturates" after some finite smoothing lag, and any further increase of h has no effect on the achievable H^∞ performance