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Mathematical Problems in Engineering
Volume 2015, Article ID 671491, 9 pages
Research Article

Robust Filtering for Discrete-Time Markov Jump Linear System with Missing Measurements

1Department of Automation, Tsinghua University, Beijing 100084, China
2Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing 100084, China

Received 28 February 2015; Accepted 28 April 2015

Academic Editor: Bo Shen

Copyright © 2015 Yingjun Niu 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.


The problem of robust filtering is investigated for discrete-time Markov jump linear system (DMJLS) with uncertain parameters and missing measurements. The missing measurements process is modelled as a Bernoulli distributed sequence. A robust filter is designed and sufficient conditions are established in terms of linear matrix inequalities via a mode-dependent Lyapunov function approach, such that, for all admissible uncertain parameters and missing measurements, the resulting filtering error system is robustly stochastically stable and a guaranteed performance constraint is achieved. Furthermore, the optimal performance index is subsequently obtained by solving a convex optimisation problem and the missing measurements effects on the performance are evaluated. A numerical example is given to illustrate the feasibility and effectiveness of the proposed filter.