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Stabilisation for positive switched T-S fuzzy delayed systems under standard L1 and L∞ performance

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  • Shuo Li
  • Zhengrong Xiang
  • Jian Guo

Abstract

In this paper, the stabilisation problem for positive switched T-S fuzzy delayed systems under standard L1 and L∞ performance is addressed. First, by proposing a time-scheduled multiple linear copositive Lyapunov function which is time-varying during the mode-dependent minimum dwell-time interval, sufficient conditions of asymptotical stability for positive switched T-S fuzzy delayed system under dwell-time switching are derived for the first time. Then, sufficient conditions for the underlying system to be asymptotically stable with standard L1 and L∞ performance are obtained, respectively. Based on the obtained results, a fuzzy state-feedback controller scheme is designed to stabilise the positive switched T-S fuzzy delayed system, while guaranteeing the positivity and asymptotical stability with standard L1 performance in closed loop. Furthermore, the stabilisation problem under standard L∞ performance is also solved. All the results are presented in the linear programming form. Finally, two numerical examples are presented to demonstrate the effectiveness of the obtained theoretical results.

Suggested Citation

  • Shuo Li & Zhengrong Xiang & Jian Guo, 2018. "Stabilisation for positive switched T-S fuzzy delayed systems under standard L1 and L∞ performance," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(6), pages 1226-1241, April.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:6:p:1226-1241
    DOI: 10.1080/00207721.2018.1442512
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    Cited by:

    1. Wang, Huajian & Qi, Wenhai & Zhang, Lihua & Cheng, Jun & Kao, Yonggui, 2020. "Stability and stabilization for positive systems with semi-Markov switching," Applied Mathematics and Computation, Elsevier, vol. 379(C).

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