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

  • Dong-Xia ZhaoEmail author
  • Jun-Min Wang
  • Ya-Ping Guo
Regular Papers Control Theory and Applications
  • 17 Downloads

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.

Keywords

Coupled system exponential stability heat equation spectral analysis 

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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNorth University of ChinaTaiyuanChina
  2. 2.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  3. 3.School of MathematicsShanxi UniversityTaiyuanChina

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