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Finite-time boundary stabilization of fractional reaction-diffusion systems
  • Run-Jie Zhang,
  • Liming Wang,
  • Kai-Ning Wu
Run-Jie Zhang
Harbin Institute of Technology Weihai

Corresponding Author:[email protected]

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Liming Wang
Harbin Institute of Technology Weihai
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Kai-Ning Wu
Harbin Institute of Technology - Weihai
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Abstract

This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are presented to ensure the FTS of FRDSs via the designed boundary controller. The effect of diffusion term of FRDSs on the FTS is also investigated. Both Neumann and mixed boundary conditions are considered. Moreover, the robust finite-time stabilization of uncertain FRDSs is studied when there are uncertainties in the system’s coefficients. Under the designed boundary controller, sufficient conditions are presented to guarantee the robust FTS of uncertain FRDSs. Finally, numerical examples are presented to verify the effectiveness of our theoretical results.
26 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
27 Dec 2021Submission Checks Completed
27 Dec 2021Assigned to Editor
08 Jan 2022Reviewer(s) Assigned
08 May 2022Review(s) Completed, Editorial Evaluation Pending
09 May 2022Editorial Decision: Revise Minor
31 May 20221st Revision Received
31 May 2022Submission Checks Completed
31 May 2022Assigned to Editor
31 May 2022Reviewer(s) Assigned
05 Jun 2022Review(s) Completed, Editorial Evaluation Pending
08 Jul 2022Editorial Decision: Revise Minor
11 Jul 20222nd Revision Received
11 Jul 2022Submission Checks Completed
11 Jul 2022Assigned to Editor
11 Jul 2022Reviewer(s) Assigned
16 Sep 2022Review(s) Completed, Editorial Evaluation Pending
26 Sep 2022Editorial Decision: Accept
08 Oct 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8786