### When does the *H_infinity* fixed-lag smoothing performance saturate?

* L. Mirkin and G. Meinsma
*

**Abstract**

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

**BibTex entry **

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