Exponential stability of a repairable system with N failure modes and K standby units

Abstract

This paper is devoted to studying the existence, uniqueness and exponential stability of repairable system's time-dependent solution. By analysis the spectrum of the system operator generated by the repairable system, we derive that zero is the unique spectral point on the imaginary axis and the other spectral lie on the left half plane. The positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equation is a quasicompact operator. As a result, we get the desired result that the dynamic solution of the system exponentially tends to the steady solution.

Exponential Asymptotic Stability of a Repairable System with Two Identical Components

“…W. W. Hu et al in [1]present exponential stability of a parallel repairable system with warm standby by the quasi-compactness and irreducibility of the semigroups. L. J. Zhao in [2] studied the exponential stability of a repairable system with two states by analyzing the essential growth bound of the system operator. By using similar L.J.…”

“…By using similar L.J. Zhao , s [2]method, S.B.Zhou in [3] discussed exponential stability of a series repairable system.In this note,we employ completely different method to show the repairable system with two identical components.…”