Exponential stability of a repairable system with imperfect switching mechanism

Weiwei Hu, Zifei Shen, Yuhong Xin, Guangtian Zhu

Research output: Contribution to journalArticlepeer-review

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Abstract

This paper is devoted to investigating the exponential stability of a kind of repairable system with cold standby units, imperfect switching mechanism and multiple non-critical and critical errors. We have known that the system operator generates a positive C0-semigroup of contractions and will show its quasi-compactness and irreducibility. Further, 0 is a simple eigenvalue of the system operator. As a result, we obtain that the time-dependent solution of the system converges to the steady-state solution exponentially, which is the positive eigenfunction corresponding to the simple eigenvalue 0.

Original languageEnglish (US)
Pages (from-to)93-102
Number of pages10
JournalAsymptotic Analysis
Volume54
Issue number1-2
StatePublished - Nov 7 2007

Keywords

  • C-semigroup
  • Essential growth bound
  • Exponential stability
  • Quasi-compact

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