西南交通大学学报 2012, 47(3) 420-426 DOI:   10.3969/j.issn.0258-2724.2012.03.011  ISSN: 0258-2724 CN: 51-1277/U

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本文关键词相关文章
M-矩阵
箱体理论
全局指数稳定性
随机关联系统
向量Lyapunov函数
本文作者相关文章
施继忠
张继业
PubMed
Article by Yi,J.Z
Article by Zhang,J.Y

一类随机非线性关联大系统的全局指数稳定性

施继忠1,2, 张继业1

1. 西南交通大学牵引动力国家重点实验室, 四川 成都 610031;
2. 巢湖学院数学系, 安徽 巢湖 238000

摘要

为研究车辆建模导致的随机误差对自动化公路车辆系统等关联大系统的影响, 将确定性箱体理论推广到随机箱体理论, 利用M-矩阵理论和随机箱体理论, 构造适当的向量Lyapunov函数,通过分析相应随机微分不等式的稳定性, 利用随机大系统的系数矩阵以及与大系统关联的Lyapunov矩阵方程的解构造判定矩阵, 得到该类大系统全局指数稳定性的充分性判据,即当判定矩阵为M-矩阵时, 大系统是全局指数稳定的. 仿真结果表明:本文算法收敛速度快, 在20 s内系统状态就能达到稳定.

关键词 M-矩阵   箱体理论   全局指数稳定性   随机关联系统   向量Lyapunov函数  

Global Exponential Stability for a Class of Stochastic Nonlinear Interconnected Large-Scale Systems

SHI Jizhong1,2, ZHANG Jiye1

1. Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China;
2. Department of Mathematics, Chaohu College, Chaohu 238000, China

Abstract:

In order to study the effects of random errors caused by vehicle modeling on interconnected large-scale systems like the automated highway vehicle system, the deterministic theory was extended to the random case theory, and a proper vector Lyapunov function was constructed using the matrix theory and the random case theory. By analyzing the stability of stochastic differential inequalities, a coefficient matrix of the random large-scale system and the solutions of the Lyapunov matrix function interconnected with large-scale system are used to construct a judgment matrix, and then obtain the sufficiency criterion for global exponential stability of the large-scale system: when the judgment matrix is a quasi-M-matrix, the global index of the large-scale system is stable. Simulation results show that the algorithm proposed in the paper has a rapid convergence rate, and the system can achieve stability in 20 s.

Keywords: M-matrix   box theory   global exponential stability   stochastic interconnected systems   vector Lyapunov function  
收稿日期 2010-06-08 修回日期  网络版发布日期 2012-05-29 
DOI: 10.3969/j.issn.0258-2724.2012.03.011
基金项目:

国家自然科学基金资助项目(50823004, 60974132, 11172247);教育部博士点基金资助项目(200806130003); 安徽省高校自然科学研究项目(KJ2011B102)

通讯作者: 张继业(1965-),男,教授,博士,研究方向为系统稳定性分析与控制、智能交通系统,电话:028-86466040, E-mail:jyzhang@swjtu.edu.cn
作者简介: 施继忠(1977-),男,博士研究生,研究方向为系统稳定性分析与控制,E-mail:shijizhong2006@126.com

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1.张克跃;任殿波;张继业.分布时滞动态神经网络的 全局指数稳定性 [J]. 西南交通大学学报, 2008,43(1): 57-61
2.任殿波;张继业 .一类时间滞后关联大系统的全局指数稳定性 [J]. 西南交通大学学报, 2005,40(3): 343-346

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