一类人为错误可修复系统的指数稳定性分析

随着科学技术的发展,特别是电子产品和网络的运用,系统的可靠性分析变得日益重要.在Dhillon B S和Yang N F(1993)中通过增补变量的方法建立了这类系统的数学模型并进行研究.在此基础上进一步讨论系统解的渐进稳定性和指数稳定性,证明了系统算子在Bnacha空间中可以转化为C_0半群,0是系统算子的简单本征值,而且是系统在虚轴上唯一的谱点.此外本文还分析了在系统扰动前后系统算子解的基本谱,结果显示系统的动态解以指数稳定性趋向于系统的稳态解,通过maple作图发现系统稳定解有时候不一定趋向于系统的实际解,这对实际运用有重要的指导意义.

Analysis of Stability and Reliability of a Class of Repairable Systems

As the development of science and technology,electron productions and network are used everywhere.So the stability analysis of the system becomes more and more important. B.S.Dhillon and N.F.Yang(1993)developed a mathematical model of a(two parrallel identical units working and one on standby)system with human error and arbitrarily distributed repair times by supplementary variable technique.This paper discussed the asymptotic stability and exponential stability of the system solution.We prove that system operators generate a positive C_0-semigroup in the state Banach space.We show that the existence of eigenvalue 0, and 0 is the unique spectral point of the system on the imaginary axis.Further,this paper analyzed the essential spectrum of the system operator before and after perturbation.The results show that the dynamic solution of the systems exponential stability and tends to the steady solution of the system.We can know that the stability of the solution is not necessarily a reliable solution of the system by Maple mapping.This is the practical application of great guiding significance.