Necessary and Sufficient Condition for Finite Horizon hEstimation of time delay systems

Huanshui Zhang, Dapeng Zhang, Lihua Xie

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

8 Citations (Scopus)


This paper is concerned with the problems of finite horizon H∞filtering, prediction and fixed-lag smoothing for linear continuous-time systems with multiple delays. By applying an innovation approach in Krein space, a necessary and sufficient condition for the existence of an H∞filter, predictor or smoother is derived. The estimator is given in terms of the solution of a partial differential equation with boundary conditions. The innovation approach in Krein space enables us to convert the very complicated deterministic estimation problem into a stochastic one to which a simple H2innovation analysis method can be adapted. The result of this paper demonstrates that the Krein space approach is powerful in solving otherwise very complicated H∞problems. Our result is in contrast with many recent sufficient conditions for H∞filtering of delay systems.
Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Number of pages6
Publication statusPublished - 1 Dec 2003
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: 9 Dec 200312 Dec 2003


Conference42nd IEEE Conference on Decision and Control
Country/TerritoryUnited States
CityMaui, HI

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


Dive into the research topics of 'Necessary and Sufficient Condition for Finite Horizon hEstimation of time delay systems'. Together they form a unique fingerprint.

Cite this