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Exponential Stability of a Reparable Multi-State Device

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Abstract

The exponential stability of a multi-state device is discussed in this paper. We present that the C 0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.

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Authors and Affiliations

  1. Beijing Institute of Information and Control, Beijing, 100037, China

    Weiwei Hu & Jingyuan Yu

  2. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Houbao Xu

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Guangtian Zhu

Authors
  1. Weiwei Hu
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  2. Houbao Xu
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  3. Jingyuan Yu
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  4. Guangtian Zhu
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Corresponding author

Correspondence to Weiwei Hu.

Additional information

The research is supported by Beijing Institute of Technology Foundation under Grant No. 20060742011.

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Hu, W., Xu, H., Yu, J. et al. Exponential Stability of a Reparable Multi-State Device. Jrl Syst Sci & Complex 20, 437–443 (2007). https://doi.org/10.1007/s11424-007-9039-9

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  • DOI: https://doi.org/10.1007/s11424-007-9039-9

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