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Type: Journal article
Title: Synchronization of stochastic reaction-diffusion systems via boundary control
Author: Wu, K.
Wang, J.
Lim, C.
Citation: Nonlinear Dynamics, 2018; 94(3):1763-1773
Publisher: Kluwer Academic Publishers
Issue Date: 2018
ISSN: 0924-090X
Statement of
Kai-Ning Wu, Jian Wang, Cheng-Chew Lim
Abstract: This paper studies the problem of mean square asymptotical synchronization and H∞ synchro- nization for coupled stochastic reaction–diffusion sys- tems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptot- ical synchronization. By virtue of Lyapunov functional method and Wirtinger’s inequality, sufficient condi- tions are obtained for ensuring mean square asymptoti- cal synchronization. When coupled SRDSs are subject to external disturbance, mean square H∞ synchroniza- tion is investigated and corresponding criterion is pre- sented under a designed boundary controller. In addi- tion to focusing on systems with Neumann bound- ary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient condi- tions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.
Keywords: Synchronization; Stochastic reaction–diffusion systems; H∞ synchronization; boundary control
Rights: © Springer Nature B.V. 2018.
DOI: 10.1007/s11071-018-4455-z
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