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

Dong Xia Zhao; Jun Min Wang; Ya Ping Guo

doi:10.1007/s12555-017-0713-y

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

Dong Xia Zhao^*, Jun Min Wang, Ya Ping Guo

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	38-45
Number of pages	8
Journal	International Journal of Control, Automation and Systems
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s12555-017-0713-y
Publication status	Published - 1 Jan 2019

Keywords

Coupled system
exponential stability
heat equation
spectral analysis

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10.1007/s12555-017-0713-y

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AU - Wang, Jun Min

AU - Guo, Ya Ping

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Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Coupled system

KW - exponential stability

KW - heat equation

KW - spectral analysis

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JF - International Journal of Control, Automation and Systems

IS - 1

ER -

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

Abstract

Keywords

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