Exponential Asymptotic Stability of a Two-Unit Standby Redundant Electronic Equipment System under Human Failure

  • Authors:

  • Xing Qiao;Zhaoxing Li;Dan Ma

  • Affiliations:

  • Department of Math., Daqing Normal University, Daqing, China 163712 and Beijing Institute of Information and Control, Beijing, China 100037;Department of Math., Daqing Normal University, Daqing, China 163712;Department of Math., Daqing Normal University, Daqing, China 163712

  • Venue:
  • ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
  • Year:
  • 2009

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Abstract

In this paper, we deal with the exponential asymptotic stability of a two-unit standby redundant electronic equipment system under human failure. First we prove that the positive contraction c 0 -semigroup {T (t )} t *** 0 which is generated by the operator corresponding to these equations is a quasi-compact operator. Then by using that 0 is an eigenvalue of the operator with algebraic index one and the c 0 -semigroup {T (t )} t *** 0 is contraction, we deduce that the spectral bound of the operator is zero. By using the above results we obtain easily the exponential asymptotic stability of the solution of the redundant system.