Finite‐time boundary stabilization of reaction‐diffusion systems

Summary In this paper, the problem of boundary finite‐time stabilization is considered for reaction‐diffusion systems (RDSs). First, a full‐domain controller is designed, and sufficient conditions are given to ensure finite‐time stability of RDSs under the designed controller. Then, for practical ap...

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Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 28; no. 5; pp. 1641 - 1652
Main Authors Wu, Kai‐Ning, Sun, Han‐Xiao, Shi, Peng, Lim, Cheng‐Chew
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 25.03.2018
Subjects
Boundary conditions
Boundary control
Computer simulation
Control stability
Control systems design
finite‐time stability
full‐domain control
reaction‐diffusion systems
Robustness (mathematics)
Stability criteria
Stabilization
uncertain reaction‐diffusion systems
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Summary:Summary In this paper, the problem of boundary finite‐time stabilization is considered for reaction‐diffusion systems (RDSs). First, a full‐domain controller is designed, and sufficient conditions are given to ensure finite‐time stability of RDSs under the designed controller. Then, for practical applications, a boundary controller is designed to obtain finite‐time stability. By virtue of the finite‐time stability lemma, criteria are presented to guarantee the finite‐time stability of RDSs for the Neumann boundary conditions and the mixed boundary conditions. As an extension to uncertain RDSs, robust finite‐time stabilization is studied, and criterion is obtained under the boundary control. Numerical simulations verify the effectiveness of the proposed design techniques.
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.3977