一类随机非线性关联大系统的全局指数稳定性  

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

作　　者：施继忠[1,2] 张继业[1] 

机构地区：[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

出　　处：《西南交通大学学报》2012年第3期420-426,共7页Journal of Southwest Jiaotong University

基　　金：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)

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.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.

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 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]