Boundary stabilisation of fractional reaction-diffusion systems with time-varying delays

This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invert...

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Bibliographic Details
Published inInternational journal of systems science Vol. 55; no. 2; pp. 209 - 221
Main Authors Mathiyalagan, K., Renugadevi, T., Zhang, Huiyan
Format Journal Article
LanguageEnglish
Published London Taylor & Francis 25.01.2024
Taylor & Francis Ltd
Subjects
Backstepping method
Boundary control
Cellular communication
fractional-order
Integral transforms
Kernel functions
Linear matrix inequalities
Mathematical analysis
Neural networks
nonlinear system
time-varying delay
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Summary:This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invertible Volterra integral transformation is used to convert the considered system into a stable target system. Different from the existing results, the stability results for fractional RDEs are discussed in the sense of the Lyapunov-Krasovskii theory and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, to show the application of the results, the proposed conditions are numerically validated over a time fractional-order reaction-diffusion cellular neural network model.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2023.2269292