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

Shuo Li, Zhengrong Xiang and Jian Guo

International Journal of Systems Science, 2018, vol. 49, issue 6, 1226-1241

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.

Date: 2018
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DOI: 10.1080/00207721.2018.1442512

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