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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 658153, 8 pages
Research Article

On Fixed-Point Smoothing for Descriptor Systems with Multiplicative Noise and Single Delayed Observations

Key Laboratory for Robot & Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China

Received 9 January 2015; Revised 5 February 2015; Accepted 5 February 2015

Academic Editor: Kun Liu

Copyright © 2015 Xiao Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Optimal fixed-point smoothing problem for the descriptor systems with multiplicative noises is considered, where instantaneous and delayed observations are available. Standard singular value decomposition is used to give the restricted equivalent delayed system, where the observations also include two different types of measurements. Reorganized innovation lemma and projection theorem are used to give the fixed-point smoother for the restricted equivalent delayed system. The fixed-point smoother is given in terms of recursive Riccati equations.