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Necessary and sufficient condition for finite horizon H estimation of time delay systems

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3 Author(s)
Huanshui Zhang ; Shenzhen Graduate Sch., Harbin Inst. of Technol., Shenzhen, China ; Huanshui Zhang ; Lihua Xie

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 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 filtering of delay systems.

Published in:

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on  (Volume:6 )

Date of Conference:

9-12 Dec. 2003