一类具有可修复储备部件的人-机系统解的指数稳定性

The exponential stability of a human-machine system with general failed system repair time distribution

针对具有2个运行部件和1个储备部件,故障修复时间服从一般分布的人-机系统模型,运用泛函分析的方法和Banach空间上的线性算子半群理论,证明了严格占优本征值的存在性,并通过分析系统本质谱界经过扰动后的变化,证明了在一定条件下系统的动态解以指数形式收敛于系统的稳态解.

We attempt to study a model of human-machine system with general failed system repair time distri- bution which have two units active and one unit on standby by using the theory of the functional analysis meth- od, especially the theory semi-groups of linear operators on Banach space. Firstly, the existence of the strictly dominance eigenvalue is proved. Then by analyzing the change of the system essential spectral bound under the perturbation, we prove that the dynamic solution is exponential tends to the steady solution of the system.