Asymptotic stability of a repairable system with imperfect switching mechanism

Asymptotic stability of a repairable system with imperfect switching mechanism

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355 maybelline fit me This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution.We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution.By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and 0 is the unique spectral point on imaginary axis.

As a result, here the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue 0.