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Mathematical Problems in Engineering
Volume 2011, Article ID 839648, 17 pages
Research Article

Robust 𝐿 𝟐 - 𝐿 ∞ Filtering of Time-Delay Jump Systems with Respect to the Finite-Time Interval

Shuping He1,2,3 and Fei Liu1,2

1Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Ministry of Education, Wuxi 214122, China
2Institute of Automation, Jiangnan University, Wuxi 214122, China
3Control Systems Centre, School of Electrical and Electronic Engineering, University of Manchester, Manchester M60 1QD, UK

Received 10 September 2010; Accepted 22 September 2010

Academic Editor: Ming Li

Copyright Β© 2011 Shuping He and Fei Liu. 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.


This paper studied the problem of stochastic finite-time boundedness and disturbance attenuation for a class of linear time-delayed systems with Markov jumping parameters. Sufficient conditions are provided to solve this problem. The 𝐿 2 - 𝐿 ∞ filters are, respectively, designed for time-delayed Markov jump linear systems with/without uncertain parameters such that the resulting filtering error dynamic system is stochastically finite-time bounded and has the finite-time interval disturbance attenuation 𝛾 for all admissible uncertainties, time delays, and unknown disturbances. By using stochastic Lyapunov-Krasovskii functional approach, it is shown that the filter designing problem is in terms of the solutions of a set of coupled linear matrix inequalities. Simulation examples are included to demonstrate the potential of the proposed results.