When does the H_infinity fixed-lag smoothing performance saturate?

L. Mirkin and G. Meinsma
A notable difference between the $H_2$ and $H_infty$ smoothing is that the achievable performance in the latter problem might ``saturate'' as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag. In this paper necessary and sufficient conditions under which such a saturation takes place are derived. In particular, it is shown that the $H_\infty$ performance saturates only if the $H_infty$ norm of the optimal error system is achieved at the infinite frequency, i.e., if the worst case disturbance is ``infinitely fast'' and thus in a sense unpredictable.

Keywords: Fixed-lag smoothing, $H_\infty$ estimation, Riccati equation.
Pdf file: IFACb02b.pdf
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