Existence and design of observers for two-dimensional linear systems with multiple channel faults

  • Liang Cao
  • Dong Zhao
  • Youqing Wang
  • Steven X. Ding


Integrated states/faults observers for two-dimensional (2-D) linear systems, which can simultaneously estimate system states and faults, are studied in this study. Multiple channel faults, occurring in both measurement equation and state equation, are considered. On the basis of the singular system observer method and stability theory, asymptotically stable observers and uniformly ultimately bounded observers are proposed for the 2-D systems. For these two cases, constructive methods for observer design and parameter tuning are further provided. Under different system conditions, the necessary and sufficient conditions for the existence of integrated observers are derived and proved through matrix rank analysis. Finally, two examples are given to demonstrate the performance of the proposed methods.


States/faults estimation Singular system observer Two-dimensional systems Asymptotically stable observer Uniformly ultimately bounded observer 



This study was supported by Shandong Province Science Fund for Distinguished Young Scholars under Grant JQ201812, the National Natural Science Foundation of China under Grant 61751307, Research Fund for the Taishan Scholar Project of Shandong Province of China, and Chinese Scholarship Council (award to Liang Cao for half year’s study at the University of Duisburg-Essen).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Liang Cao
    • 1
    • 3
  • Dong Zhao
    • 1
    • 3
  • Youqing Wang
    • 2
  • Steven X. Ding
    • 3
  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.College of Electrical Engineering and AutomationShandong University of Science and TechnologyQingdaoChina
  3. 3.Institute for Automatic Control and Complex Systems (AKS), University of Duisburg-EssenDuisburgGermany

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