4.4 Article

Boundary Mittag-Leffler stabilization of a class of time fractional-order nonlinear reaction-diffusion systems

Journal

ASIAN JOURNAL OF CONTROL
Volume 25, Issue 5, Pages 3699-3714

Publisher

WILEY
DOI: 10.1002/asjc.3062

Keywords

boundary control; LMIs; M-L stability; time FNRDSs; well-posedness

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This paper considers the boundary control design of time fractional-order nonlinear reaction-diffusion systems (FNRDSs) in three cases: domain-averaged measurement, collocated boundary point measurement, and anti-collocated boundary point measurement. Boundary controllers are directly designed based on the measurements for domain-averaged measurement and collocated boundary point measurement. For anti-collocated boundary point measurement, an observer is constructed first to overcome the difficulty of using the measurement directly, and then an observer-based boundary controller is designed. Sufficient conditions for the Mittag-Leffler (M-L) stability of the closed-loop system are provided in terms of linear matrix inequalities (LMIs). Numerical simulation results are provided to demonstrate the feasibility and effectiveness of the proposed methods.
Boundary control design of a class of time fractional-order nonlinear reaction-diffusion systems (FNRDSs) is considered in three cases: domain-averaged measurement, collocated boundary point measurement, and anti-collocated boundary point measurement. For domain-averaged measurement and collocated boundary point measurement, boundary controllers are designed directly based on the measurements, respectively. For the anti-collocated boundary point measurement, to overcome the difficulty that the measurement cannot be used for the controller design directly, an observer is constructed firstly, and then, an observer-based boundary controller is designed. Sufficient conditions for Mittag-Leffler (M-L) stability of the closed-loop system are all provided in terms of linear matrix inequalities (LMIs). Numerical simulation results are provided to illustrate the feasibility and effectiveness of the proposed methods.

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