Robust stability analysis for discrete and distributed time-delays Markovian jumping reaction-diffusion integro-differential equations with uncertain parameters

Advances in Difference Equations

Xiaogang Yang¹  Ruofeng Rao¹  Xiongrui Wang²  Shouming Zhong³ 

[1] Department of Mathematics, Chengdu Normal University, Chengdu, China;Institution of Mathematics, Yibin University, Yibin, China;School of Science Mathematics, University of Electronic Science and Technology of China, Chengdu, China

关键词: exponential stability;    Laplace diffusion;    distributed time-delays;    M-matrix;    Lyapunov functional;   

DOI  :  10.1186/s13662-015-0526-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the authors employ Lyapunov stability theory, and the M-matrix, H-matrix, and linear matrix inequality (LMI) techniques and variational methods to obtain the LMI-based stochastically exponential robust stability criterion for discrete and distributed time-delays Markovian jumping reaction-diffusion integro-differential equations with uncertain parameters, whose background of physics and engineering is bidirecional associative memory (BAM) neural networks. It is worth mentioning that an LMI-based stability criterion can easily be computed by the Matlab toolbox which has high efficiency and other advantages in large-scale engineering calculations. Since using the M-matrix and H-matrix methods is not easy in obtaining the LMI criterion conditions, the methods employed in this paper improve those of previous related literature to some extent. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.

【 授权许可】

CC BY