The Asymptotic Stability of a System with Two Identical Robots and a Built-In Safety

In this paper, we study the asymptotic behavior of a repairable system with two identical robots and a built-in safety. First, the integro-differential equations described the system was transformed into some abstract Cauchy problem. Second, by the positive c₀-semigroups which is generated by the generator A+E. Last, by studying spectral properties of the operator corresponding to this system. As a result of the stability of c₀-semigroup theory of linear operators, we show that the dynamic availability of the system converge the steady availability as time tends to infinity. We obtain the asymptotic stability of the solution of the repairable system.