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The Direct Feedback Control and Exponential Stabilization of a Coupled Heat PDE-ODE System with Dirichlet Boundary Interconnection

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  • Control Theory and Applications
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Abstract

This paper addresses the exponential stability for an interconnected system of an nth-order ODE system with the input governed by the Dirichlet boundary of a heat equation, and conversely, the output of the ODE is fluxed into the heat equation. The semigroup approach is adopted to show that the system operator is well-posed. We establish the exponential stability of the system by Riesz basis method. Furthermore, with MATLAB software, some numerical simulations are presented to show the effectiveness of the interconnection between the heat PDE and ODE systems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, North University of China, Taiyuan, 030051, China

    Dong-Xia Zhao

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Jun-Min Wang

  3. School of Mathematics, Shanxi University, Taiyuan, 030006, China

    Ya-Ping Guo

Authors
  1. Dong-Xia Zhao
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  2. Jun-Min Wang
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  3. Ya-Ping Guo
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Corresponding author

Correspondence to Dong-Xia Zhao.

Additional information

Recommended by Associate Editor Soohee Han under the direction of Editor PooGyeon Park.

Dong-Xia Zhao received the Ph.D. degree in Applied Mathematics from Beijing Institute of Technology in 2013. Since 2016, she has been an associate professor at North University of China in school of science. Her research interests focus on the control theory of distributed parameter systems.

Jun-Min Wang received his B.S. degree in Mathematics from Shanxi University in 1995, and an M.S. degree in Applied Mathematics from Beijing Institute of Technology in 1998, respectively, and a Ph.D. degree in Applied Mathematics from the University of Hong Kong in 2004. From 1998 to 2000, he worked as a teaching assistant at the Beijing Institute of Technology. He was a postdoctoral fellow at the University of the Witwatersrand, South Africa from 2004 to 2006. From 2006 to 2009 he was an associate professor at the Beijing Institute of Technology. Since 2009, he has been with Beijing Institute of Technology as a full professor in Applied Mathematics and Control Theory. His research interests focus on the control theory of distributed parameter systems. Dr. Wang is IEEE senior member and the recipient for New Century Excellent Talents Program from Ministry of Higher Education of China.

Ya-Ping Guo received the Ph.D. degree in Applied Mathematics from Beijing Institute of Technology in 2016. Since 2016, she has been a teaching assistant at Shanxi University in school of Mathematics. Her research interests focus on the control theory of distributed parameter systems.

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Zhao, DX., Wang, JM. & Guo, YP. The Direct Feedback Control and Exponential Stabilization of a Coupled Heat PDE-ODE System with Dirichlet Boundary Interconnection. Int. J. Control Autom. Syst. 17, 38–45 (2019). https://doi.org/10.1007/s12555-017-0713-y

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  • DOI: https://doi.org/10.1007/s12555-017-0713-y

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