Stability Analysis of the Multistate Gas Power Repairable System

In this paper, a multistate gas power repairable system by the supplementary variable method and Markov process theory is studied. Through the spectral analysis of the system operator, it is proved that 0 is the only spectral point on the imaginary axis, and the unique nonnegative solution of the system is obtained. At the same time, it is proved that the nonnegative time dependent solution of the system converges to the steady-state solution of the system when the time approaches infinity, so that the asymptotic stability of the multistate gas electric repairable system is obtained. And it verifies the correctness of the theory by using numerical calculations in this paper.