Exponential stability of a reparable multi-state device

Weiwei Hu, Houbao Xu, Jingyuan Yu, Guangtian Zhu

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36 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)437-443
Number of pages7
JournalJournal of Systems Science and Complexity
Issue number3
StatePublished - Sep 2007

Bibliographical note

Funding Information:
Beijing Institute of Information and Control, Beijing 100037, China. Email: huww51@yahoo.com.cn. Houbao XU Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China. Jingyuan YU Beijing Institute of Information and Control, Beijing 100037, China. Guangtian ZHU Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China. ∗The research is supported by Beijing Institute of Technology Foundation under Grant No. 20060742011.


  • C -semigroup
  • Exponential stability
  • Irreducibility
  • Quasi-compact


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