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讨论具有临界和非临界操作错误的可修复人机系统．利用系统算子生成的Banach 空间中的正压缩C0半群的性质,证明了此系统的唯一非负时间依赖解恰是系统算子0本征值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一个直接结果,得出了该可修人机系统的渐近稳定性．
Discuss repairable human-machine systems with critical and non-critical operational errors. By using the properties of positive-contracted C0 semigroups in Banach spaces generated by system operators, we prove that the unique nonnegative time-dependent solution of this system is just the normalized eigenvector corresponding to the eigenvalue of system operator 0. At the same time, The analysis of the distribution of spectral points of the system operators proves that the spectral points of the system operators lie in the left half plane of the complex plane and there is no other spectrum except the zero point on the imaginary axis as a direct result of the stability of the semigroups of linear operators , We get the asymptotic stability of the repairable man-machine system.