Asymptotic stability of a repairable system with imperfect switching mechanism

Houbao Xu, Weihua Guo, Jingyuan Yu and Guangtian Zhu

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-13

Abstract:

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 C 0 -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, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue 0 .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:106169

DOI: 10.1155/IJMMS.2005.631

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