一类串联可修复系统的稳态解  

The Asymptotic Stability of a Series Repairable System

作　　者：徐厚宝[1] 郭卫华[2] 于景元[3] 朱广田[4] 

机构地区：[1]北京理工大学数学系,北京100081 [2]郑州轻工业学院信息与计算科学系,河南郑州463000 [3]北京信息控制研究所,北京100037 [4]中科院数学与系统科学研究院,北京100080

出　　处：《应用数学学报》2006年第1期46-52,共7页Acta Mathematicae Applicatae Sinica

摘　　要：本文讨论了一类具有两不同部件串联的可修复系统。利用系统算子生成的Banach空间中的正压缩C_o半群的性质,证明了系统的非负稳态解恰是系统算子的0本征值所对应的规范化后的本征向量；同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的—个直接结果,得出了该串联可修复系统的渐近稳定性。Stable solution of a repairable system associated with two non-identical units is studied in this paper. The stable solution is derived by the positive C0-semigroup which is generated by system operator and this solution is proved to be the eigenvector responding to the eigenvalue 0. What＇s more, 0 is showed to be the unique spectral point of the system operator on the imaginary axis. As a result, the asymptotic stability of the system is obtained.

关 键 词：串联系统 C0半群 稳态解 

分 类 号：O177.29[理学—数学]