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Asymptotic stability of a repairable system with imperfect switching mechanism

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  • Houbao Xu
  • Weihua Guo
  • Jingyuan Yu
  • Guangtian Zhu

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 .

Suggested Citation

  • Houbao Xu & Weihua Guo & Jingyuan Yu & Guangtian Zhu, 2005. "Asymptotic stability of a repairable system with imperfect switching mechanism," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:106169
    DOI: 10.1155/IJMMS.2005.631
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