讨论了一个可靠机器,一个不可靠机器和一个缓冲库构成的计算机集成系统(CIMS),利用由该系统所决定的算子A+E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+E的0本征值所对应的规范化后的本征向量;同时通过对算子A+E的谱点分布的分析,证明了算子A+E的谱点均位于左半平面且在虚轴上除0点外无谱,作为线性算子半群稳定性的一个直接结果,得出了该系统解的渐近稳定性.

We study the asymptotic behavior of atransfer line with a reliable machine, an unreliable machine and astorage buffer. By the positive $C_0$ semigroup which is generated by the A+E, we show that there exists a steady nonnegative solution of the system which is just the normalized eigenvector of operator A+E corresponding to eigenvalue 0. By spectral analysis of A+E , we prove that there is no spectrum of A+E on the imaginary axis except 0. As a result of the stability of semigroup theory o...