一类可修的人机系统解的渐近稳定性  

Asymptotic Stability of the Solution of a Repairable Human & Machine System

作　　者：郭卫华[1] 吴松丽[2] 徐厚宝[3] 

机构地区：[1]郑州轻工业学院信息与计算科学系,河南郑州463000 [2]驻马店教育学院数学系,河南驻马店450002 [3]北京信息控制研究所,北京100037

出　　处：《系统工程理论与实践》2004年第8期91-95,共5页Systems Engineering-Theory & Practice

基　　金：河南省教育厅自然科学基金(2000110014)

摘　　要：　研究了两相同部件温储备可修的人机系统,利用由该系统所决定的算子A+B生成的Banach空间中的正压缩C0半群,证明了此系统的非负稳定解恰是算子A+B的.本征值对应的本征向量,同时通过研究算子A+B的谱特征,得到了算子A+B的谱点均位于复平面的左半平面且在虚轴上除0点外无谱的结论,进而得到了该系统的渐近稳定性.In this paper, we study the asymptotic behavior of a warm standby repairable human-machine system with two identical units. By the positive C_0-semigroup which is generated by the operator A+B, we show that there exists a steady nonnegative solution of the system which is just the normalized eigenvector of operator A+B corresponding to eigenvalue 0. By studying spectral properties of the operator A+B, we prove that there is no spectrum of A+B on the imaginary axis except 0. As a result of the stability of semigroup theory of linear operators, we get the asymptotic stability of this system.

关 键 词：人机系统 本征值 谱 渐近稳定性 

分 类 号：O175.2[理学—数学]