两部件退化备用可修复系统指数稳定性分析  

Exponential stability analysis of a two unit deteriorating standby modified system

作　　者：彭培让[1] 

机构地区：[1]河南教育学院数学系,郑州450046

出　　处：《河南理工大学学报（自然科学版）》2012年第5期633-636,共4页Journal of Henan Polytechnic University（Natural Science）

基　　金：河南省科技厅基础与前沿技术研究项目(122300410116);河南省教育厅自然科学基金资助项目(128140018)

摘　　要：运用泛函分析的方法和Banach空间上的线性算子半群理论,研究了两部件退化备用可修复系统的指数稳定性.首先证明了该系统存在严格占优本征值,而后通过对系统本质谱的增长性约束以及经扰动本质谱半径变化的分析,证明了该系统的时间依赖解指数收敛于系统的稳态解.The exponential stability analysis of a two unit deteriorating standby modified system is studied by the method of functional analysis and the theory of a linear-operator semi-group that is on the Banach space.Firstly,the existence of rigorous dominant eigenvalue is proved,then that the time-dependent solution of the system converging exponentially to the static solution of the system is proved by analyzing the restriction of the growth of the system operator essential spectrum and the change of the system operator essential spectral radius after disturbance.

关 键 词：严格占优本征值 本质谱 扰动 指数稳定性 

分 类 号：O175.21[理学—数学]