【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.更多还原

【Abstract】 In this paper, we study the asymptotic behavior of a warm standby repairable human-machine system with two identical units. By the positive C₀-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.更多还原