# When does the $H^\infty$ fixed-lag smoothing performance saturates?

Leonid Mirkin, Gjerrit Meinsma

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

## 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 note necessary and sufficient conditions under which such a saturation occurs 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 for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable.
Original language Undefined Proceedings of the 15th IFAC World Congress Barcelona, Spanje Elsevier 121-124 4 978-0-08-044295-2 Published - 2002 15th IFAC World Congress 2002 - Barcelona, SpainDuration: 21 Jul 2002 → 26 Jul 2002Conference number: 15http://folk.ntnu.no/skoge/prost/proceedings/ifac2002/home.htm

### Publication series

Name Elsevier

### Conference

Conference 15th IFAC World Congress 2002 Spain Barcelona 21/07/02 → 26/07/02 http://folk.ntnu.no/skoge/prost/proceedings/ifac2002/home.htm

## Keywords

• METIS-210619
• Riccati equation
• EWI-16738
• $H_\infty$ estimation
• Fixed-lag smoothing
• IR-69139