具有热储备的可修复平行系统在由常规错误引起失效下的渐进稳定性

讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用Banach空间的Volttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是mild解.但在t＞0时系统古典解存在唯一,所以此时mild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性.

Asymptotic Stability of a Parallel Reparable System with Warm Standby under Common-cause Failure

This paper presents the asymptotic stability of a two identical unit parallel system with a warm standby subject to common-cause failures. First, we obtain the existence and uniqueness of the nonnegative time-dependent solution of the system by using the Volterra operator equation in Banach space. Second, we use the C0-semigroup theory of linear operators to prove the existence and uniqueness of the positive time-dependent solution of the model, which is a mild solution for the initial value is not in the domain. However, it equals to the classical solution whent ＞ 0. As a result of the stability of C0-semigroup theory of linear operators, we get the time-dependent solution converging to its static solution in the sense of the norm, thus obtain the asymptotic stability of the solution of this system.