非线性大系统的部分稳定性研究  

On Partial Stability of Nonlinear Large Scale Systems

作　　者：蹇继贵[1] 罗海庚[1] 廖伍代[2] 廖晓昕[1] 

机构地区：[1]华中科技大学控制科学与工程系 [2]军事经济学院基础部,武汉430035

出　　处：《重庆工学院学报》2004年第6期45-48,共4页Journal of Chongqing Institute of Technology

基　　金：国家自然科学基金资助项目(60274007);高等学校博士点基金资助项目(20010487005)

摘　　要：研究了孤立子系统分别为定常线性和非线性非自治系统的两类大系统的部分稳定性。利用不等式分析技巧和构造出合适的Lyapunov函数,分别获得了两类大系统的平凡解关于部分变元一致稳定、渐近稳定和指数稳定的代数判据,特别地,对于仅含有两个子系统的大系统,通过Hur witz判别方法得到了其平凡解部分渐近稳定和部分指数稳定的简单代数判据。In this paper, partial stability of the two classes of large-scale systems are discussed, where isolated subsystems are linear and nonlinear non-autonomous, respectively. Based on inequalities analysis technique and appropriate Lyapunov functions constructed, some theorems concerning partial uniform stability, partial asymptotic stability and partial exponential stability for the classes of large-scale systems are obtained. In special cases, some simple algebraic criterion of partial asymptotic stability and partial exponential for large-scale systems containing only two subsystems are also derived by Hurwitz criterion.

关 键 词：平凡解 代数判据 部分变元 非线性非自治系统 一致稳定 非线性大系统 孤立子 渐近稳定 Lyapunov函数 指数稳定 

分 类 号：O175[理学—数学] TP13[理学—基础数学]