Abstract
The L 2–L ∞ filtering problem for continuous-time polytopic uncertain stochastic time-delay systems is investigated. The main purpose is to design a full-order filter guaranteeing a prescribed L 2–L ∞ attenuation level for the filtering error system. A simple alternative proof is given for an enhanced LMI (linear matrix inequality) representation of L 2–L ∞ performance. Based on the criterion which keeps Lyapunov matrices out of the products of system dynamic matrices, a sufficient condition for the existence of a robust estimator is formulated in terms of LMIs. The corresponding filter design is cast into a convex optimization problem. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.
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Recommended by Editorial Board member Bin Jiang under the direction of Editor Young Il Lee. This work was supported by the National Natural Science Foundation of China (No. 60772046, 60904031 and 60974044), Natural Science Foundation of Guangdong Province (No. 9451805707002681), Basic Research Plan in Shenzhen City (No. JC200903120195A) and Science Research Fund for Young Teachers in Harbin University of Science and Technology (No. 2008XQJZ021).
Ying Zhang received her M.Eng. degree in control theory and control engineering from Harbin University of Science and Technology, PRC, in 2003, and her Ph.D. degree in Control Science and Engineering in 2007 from Harbin Institute of Technology, PRC. In April 2003, she joined Harbin University of Science and Technology as an assistant teacher. She is currently a post-doctoral student in Shenzhen Graduate School, Harbin Institute of Technology. Her research interests include robust control, filter theory, and time-delay systems.
Ai-Guo Wu received his B.Eng. degree in Automation in 2002, M. Eng. degree in Navigation, Guidance, and Control in 2004, and Ph.D. degree in Control Science and Engineering in 2008 all from Harbin Institute of Technology, PRC. In October 2008, he joined Harbin Institute of Technology Shenzhen Graduate School as an assistant professor. He has served as a general secretary of the 25th Chinese Control Conference at Harbin, PRC, in 2006. His research interests include observer design, descriptor linear systems, and robust control and estimation.
Guang-Ren Duan received his B.Sc. degree in applied mathematics, and his M.Sc. and Ph.D. degrees in Control Systems Theory. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, where he became a professor of control systems theory in 1991. He visited the University of Hull, UK, and the University of Sheffield, UK, from December 1996 to October 1998, and worked at the Queen’s University of Belfast, UK, from October 1998 to October 2002. Since August 2000, he has been elected specially employed professor at Harbin Institute of Technology, PRC, sponsored by the Cheung Kong Scholars Program of the Chinese government. He is currently the director of the Center for Control Theory and Guidance Technology at Harbin Institute of Technology. He is a charted engineer in the UK, a senior member of IEEE, and a fellow of IEE. His research interests include robust control, eigenstructure assignment, descriptor systems, missile autopilot design, and magnetic bearing control.
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Zhang, Y., Wu, AG. & Duan, GR. Improved L 2–L ∞ filtering for stochastic time-delay systems. Int. J. Control Autom. Syst. 8, 741–747 (2010). https://doi.org/10.1007/s12555-010-0405-3
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DOI: https://doi.org/10.1007/s12555-010-0405-3