Achievable H-infinity performance in sampled-data smoothing: beyond the parallel to(D)over-arc(1)parallel to-barrier

摘要

The lifting technique is a powerful tool for handling the periodically time-varying nature of sampled-data systems. Yet all known solutions of sampled-data H-infinity problems are limited to the case when the feedthrough part of the lifted system, (D) over cap (1) : L-2 [0, h] --> L-2[0, h], satisfies (D) over cap (1) < gamma, where gamma is the required H-infinity performance level. While this condition is always necessary in feedback control, it might be restrictive in signal processing applications, where some amount of delay or latency between measurement and estimation can be tolerated. In this paper, the sampled-data H-infinity fixed-lag smoothing problem with a smoothing lag of one sampling period is studied. The problem corresponds to the a-posteriori filtering problem in the lifted domain and is probably the simplest problem for which a smaller than (D) over cap (1) H-infinity performance level is achievable. The necessary and sufficient solvability conditions derived in the paper are compatible with those for the sampled-data filtering problem. This result extends the scope of applicability of the lifting technique and paves the way to the application of sampled-data methods in digital signal processing. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 21]