Exponential Asymptotic Stability of a Repairable System with Two Identical Components

Abstract

The repairable system solution’s exponential asymptotic stability was discussed in this paper, First we prove that the positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equations describing a system with two identical components is a quasi-compact operator. Following the result that 0 is an eigenvalue of the operator with algebraic index one and the strongly continuous semi-group is contraction, we deduce that the spectral bound of the operator is zero. By the above results we obtain easily the exponential asymptotic stability of the solution of the repairable system.