两部件并联维修系统解的渐近稳定性

Asymptotic Stability of Solution for a Parallel Maintenance System with Two Components

研究了两部件并联维修系统,在系统非负解存在惟一的基础上,利用系统算子生成的Banach空间中的正压缩C0半群,证明了系统的非负稳定解恰是系统算子0本征值对应的非负本征向量.同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐近稳定性.

Asymptotic behavior of a parallel maintenance system with two components is studied. With the positive Co semigroup generated by the system operator, we show that the unique and nonnegative solution of system is the eigenvcctor of System operator corresponding to eigenvalue 0. By spectral analysis of the system, we find that 0 is the unique spectral point of system on the imaginary axis. As a result, the asymptotic stability of such maintenance system is obtained.