Exponential Asymptotic Stability of a Repairable System with Two Identical Components

Abstract:

The repairable system solution’s exponential asymptotic stability was discussed in this paper, First we prove that the positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equations describing a system with two identical components is a quasi-compact operator. Following the result that 0 is an eigenvalue of the operator with algebraic index one and the strongly continuous semi-group is contraction, we deduce that the spectral bound of the operator is zero. By the above results we obtain easily the exponential asymptotic stability of the solution of the repairable system.

• Periodical: Advanced Materials Research (Volumes 591-593)
• Pages: 2428-2431
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.591-593.2428
• Online since: November 2012
• Authors: Xue Feng, Ping Zuo, Hong Tu Hua, Xiao Yan Qi
• Keywords: Exponential Asymptotic Stability, Positive Contraction Strongly Continuous Semigroup, Quasi-Compact Operator

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DOI: 10.1016/0026-2714(95)00132-8

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