Boundary stabilization of random reaction-diffusion systems

被引：0

作者：

Xue, Zhuo ^{[1
]}

Wu, Kai-Ning ^{[1
]}

Wu, Zhaojing ^{[2
]}

Wu, Yongxin ^{[3
]}

机构：

[1] Harbin Inst Technol, Dept Math, Weihai 264209, Peoples R China

[2] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China

[3] Univ Bourgogne Franche Comte, FEMTO ST Inst, ENSMM, 24 Rue Savary, F-25000 Besancon, France

来源：

NONLINEAR DYNAMICS | 2025年

基金：

中国国家自然科学基金;

关键词：

Random nonlinear differential equations; Reaction-diffusion systems; Boundary stabilization; Asymptotic stability; GROSSBERG NEURAL-NETWORKS; STABILITY ANALYSIS; SYNCHRONIZATION; DELAYS;

D O I：

10.1007/s11071-024-10813-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The boundary stabilization of a class of reaction-diffusion systems perturbed by second-order processes is investigated in this work. It extends the results from random ordinary differential equations to random reaction-diffusion systems (RRDSs). First, the stability analysis of RRDSs with boundary function is presented. Using the Lyapunov method and stochastic process estimation, two criteria of asymptotic stability are established in 2-nd moment and in probability, by applying Wirtinger's inequality and the weak law of large numbers. Second, based on the obtained stability criteria, a class of boundary control problems is solved by constructing a Lyapunov functional and designing integral boundary controllers. Additionally, the influence of nonlinear terms and the diffusion coefficient on stability is analyzed. Finally, numerical simulations demonstrate the effectiveness of the boundary controller.

引用

页数：13

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