关于开或闭模型的指数稳定性  

Stability Analysis of the Open or Close Models

作　　者：张丽燕[1] 姜英秀[2] 张玉峰[1] 

机构地区：[1]延边大学理学院数学系,吉林延吉133002 [2]延边大学教务处,吉林延吉133002

出　　处：《数学的实践与认识》2011年第10期130-144,共15页Mathematics in Practice and Theory

摘　　要：讨论了系统解的渐进稳定性和指数稳定性,证明了系统在Banach空间中生成正的C_0-半群以及系统算子0本征值的存在性,系统算子的谱点均为于复平面的左半平面且在虚轴上除0外无谱,并通过分析系统本质谱界经过扰动后的变化,进一步表明在一定条件下,系统的动态解以指数形式收敛于系统的稳态解.This paper discussed the asymptotic stability and exponential stability of the system solution.We prove that system operators generate a positiveC_0-semigroup in the state Banach space.We show that the existence of eigenvalue 0,and 0 is the unique spectral point of the system on the imaginary axis.Further,this paper analyzed the essential spectrum of the system operator before and after perturbation.The results show that the dynamic solution of the systems exponential stability and tends to the steady solution of the system.

关 键 词：CO-半群 存在唯一性 预解式 简单本征值 渐进稳定性 指数稳定性 

分 类 号：O213.2[理学—概率论与数理统计]