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Title: Necessary and sufficient condition for finite horizon H[sub ∞] estimation of time delay systems
Authors: Zhang, H
Zhang, DD 
Xie, L
Keywords: Boundary conditions
Error analysis
Matrix algebra
Partial differential equations
Problem solving
Random processes
Riccati equations
Theorem proving
Issue Date: 2003
Publisher: IEEE
Source: 42nd IEEE Conference on Decision and Control : December 9-12, 2003, Maui, Hawaii, USA : proceedings, v. 6, p. 5735-5740 How to cite?
Abstract: This paper is concerned with the problems of finite horizon H[sub ∞] 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[sub ∞] 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 H₂ innovation 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[sub ∞] filtering of delay systems.
ISBN: 0-7803-7924-1
Rights: © 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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