Necessary and Sufficient Condition for Finite Horizon h∞Estimation of time delay systems

Huanshui Zhang; Dapeng Zhang; Lihua Xie

doi:10.1109/CDC.2003.1271919

Necessary and Sufficient Condition for Finite Horizon h_∞Estimation of time delay systems

Huanshui Zhang
, Dapeng Zhang
, Lihua Xie

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

8 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Pages	5735-5740
Number of pages	6
Volume	6
DOIs	https://doi.org/10.1109/CDC.2003.1271919
Publication status	Published - 1 Dec 2003
Event	42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: 9 Dec 2003 → 12 Dec 2003

Conference

Conference	42nd IEEE Conference on Decision and Control
Country/Territory	United States
City	Maui, HI
Period	9/12/03 → 12/12/03

ASJC Scopus subject areas

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

More information

10.1109/CDC.2003.1271919

Cite this

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title = "Necessary and Sufficient Condition for Finite Horizon h∞Estimation of time delay systems",

abstract = "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.",

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Necessary and Sufficient Condition for Finite Horizon h_∞Estimation of time delay systems. / Zhang, Huanshui; Zhang, Dapeng; Xie, Lihua.
Proceedings of the IEEE Conference on Decision and Control. Vol. 6 2003. p. 5735-5740.

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

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AB - 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.

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