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Global robustness for max-plus linear systems

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  • Cailu Wang
  • Yuegang Tao

Abstract

Robustness analysis is a fundamental problem in the area of formal method, systems theory and performance evaluation. This paper investigates the global robustness of max-plus linear systems, which requires all state variables are entirely unaffected by the bounded parameter perturbations. The variable element is introduced to describe the global robustness. The relationship between solvable entries and solutions of systems of max-plus linear equations is further studied to find the variable elements of max-plus linear systems. It is pointed out that any non-solvable entry is a variable element. At the same time, the global robustness is used to analyse the stability of gene regulatory networks in biology systems and the time invariance of production processes in flexible manufacturing systems. Some numerical examples are given to illustrate the results.

Suggested Citation

  • Cailu Wang & Yuegang Tao, 2017. "Global robustness for max-plus linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(15), pages 3225-3232, November.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:15:p:3225-3232
    DOI: 10.1080/00207721.2017.1381890
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    References listed on IDEAS

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    1. Geert Jan Olsder, 2011. "On the existence of periodic behaviour of switched linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(6), pages 1035-1045.
    2. Ying Shang, 2013. "Towards geometric control of max-plus linear systems with applications to queueing networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 34-49.
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