Asymptotic Stability of a Parallel Reparable System with Warm Standby under Common-cause Failure
Weiwei Hu · Acta Analysis Functionalis Applicata · 2006
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 C_0-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 when t0.As a result of the stability of C_0-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.