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Output feedback stabilization of an unstable wave equation with observations subject to time delay

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Abstract

This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition, in which observations are subject to arbitrary fixed time delay. The observability inequality indicates that the open-loop system is observable, based on which the observer and predictor are designed: The state of system is estimated with available observation and then predicted without observation. After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method. The equivalent system together with the design of observer and predictor give the estimated output feedback. It is shown that the closed-loop system is exponentially stable. Numerical simulations are presented to illustrate the effect of the stabilizing controller.

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Authors and Affiliations

  1. College of Science, North China University of Technology, Beijing, 100144, China

    Kunyi Yang, Xiang Ren & Jie Zhang

Authors
  1. Kunyi Yang
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  2. Xiang Ren
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  3. Jie Zhang
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Corresponding author

Correspondence to Kunyi Yang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61203058, the Training Program for Outstanding Young Teachers of North China University of Technology under Grant No. XN131, the Construction Plan for Innovative Research Team of North China University of Technology under Grant No. XN129, and the Laboratory construction for Mathematics Network Teaching Platform of North China University of Technology under Grant No. XN041.

This paper was recommended for publication by Editor SUN Jian.

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Yang, K., Ren, X. & Zhang, J. Output feedback stabilization of an unstable wave equation with observations subject to time delay. J Syst Sci Complex 29, 99–118 (2016). https://doi.org/10.1007/s11424-016-5169-2

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  • DOI: https://doi.org/10.1007/s11424-016-5169-2

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