The well-posedness and stability of a repairable standby human–machine system

In this paper, the solution of a standby human–machine system is investigated. By using the method of functional analysis, especially, the linear operator theory and the C 0 semigroup theory on Banach space, we prove the well-posedness and the existence of a positive solution of the system. And under some appropriate hypotheses, we study the asymptotic stability of solution of the system.