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Reset stabilisation of positive linear systems

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  • Xudong Zhao
  • Yunfei Yin
  • Jun Shen

Abstract

In this paper, the problems of reset stabilisation for positive linear systems (PLSs) are investigated. Some properties relating to reset control of PLSs are first revealed. It is shown that these properties are different from the corresponding ones of general linear systems. Second, a class of periodic reset scheme is designed to exponentially stabilise an unstable PLS with a prescribed decay rate. Then, for a given PLS with reset control, some discussions on the upper bound of its decay rate are presented. Meanwhile, the reset stabilisation for PLSs in a special case is probed as well. Finally, two numerical examples are used to demonstrate the correctness and effectiveness of the obtained theoretical results.

Suggested Citation

  • Xudong Zhao & Yunfei Yin & Jun Shen, 2016. "Reset stabilisation of positive linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 2773-2782, September.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:12:p:2773-2782
    DOI: 10.1080/00207721.2015.1022889
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    References listed on IDEAS

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    1. Jinxing Lin & Shumin Fei & Zhifeng Gao, 2013. "Control discrete-time switched singular systems with state delays under asynchronous switching," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(6), pages 1089-1101.
    2. Weiming Xiang & Jian Xiao, 2011. "filtering for switched nonlinear systems under asynchronous switching," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(5), pages 751-765.
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    Cited by:

    1. Leipo Liu & Hao Xing & Xiangyang Cao & Zhumu Fu & Shuzhong Song, 2018. "Guaranteed Cost Finite-Time Control of Discrete-Time Positive Impulsive Switched Systems," Complexity, Hindawi, vol. 2018, pages 1-8, April.
    2. Qi, Wenhai & Zong, Guangdeng & Cheng, Jun & Jiao, Ticao, 2019. "Robust finite-time stabilization for positive delayed semi-Markovian switching systems," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 139-152.

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