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Stability and stabilization of a delayed PIDE system via SPID control

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Abstract

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger’s inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61273012, 61403179, 61304023 and 61503171, in part by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2014AL009, ZR2014CP008 and ZR2015FL021, in part by Academic Team Construction of Linyi University under Grant No. 51715015, in part by Commercial Logistics Research Center of Linyi University under Grant No. 51715020, and in part by the AMEP of Linyi University.

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Authors and Affiliations

  1. School of Informatics, Linyi University, Linyi, 276005, People’s Republic of China

    Chengdong Yang & Xiao Chen

  2. School of Automation, Southeast University, Nanjing, 210096, People’s Republic of China

    Chengdong Yang

  3. School of Automobile Engineering, Linyi University, Linyi, 276005, People’s Republic of China

    Ancai Zhang

  4. School of Science, Linyi University, Linyi, 276005, People’s Republic of China

    Xiangyong Chen & Jianlong Qiu

Authors
  1. Chengdong Yang
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  2. Ancai Zhang
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  3. Xiao Chen
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  4. Xiangyong Chen
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  5. Jianlong Qiu
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Corresponding authors

Correspondence to Chengdong Yang or Jianlong Qiu.

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Yang, C., Zhang, A., Chen, X. et al. Stability and stabilization of a delayed PIDE system via SPID control. Neural Comput & Applic 28, 4139–4145 (2017). https://doi.org/10.1007/s00521-016-2297-5

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  • DOI: https://doi.org/10.1007/s00521-016-2297-5

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