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The impulse analysis of the T-S fuzzy singular system via Kronecker index

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  • Zhenghong Jin
  • Qingling Zhang
  • Xinyou Meng

Abstract

The problem of impulse analysis is considered for the T-S fuzzy singular system by using the Kronecker index and the generalised Kronecker index in this paper. The T-S singular system is divided into two cases: the uniformly regular T-S fuzzy singular system and the non-uniformly regular T-S fuzzy singular system. The contribution of this paper is twofold. First, a new definition of the generalised Kronecker form is introduced, and the algorithm of finding the generalised Kronecker form is given. Second, two theorems are proved, one is that the uniformly regular T-S fuzzy singular system is impulsive if and only if the Kronecker index is greater than one, the other one is the non-uniformly regular T-S fuzzy singular system is impulsive if and only if the generalised Kronecker index is greater than one. Finally, two numerical simulations and the population model with stage structure are carried out to show the consistency with theoretical analysis and illustrate the effectiveness of the algorithm.

Suggested Citation

  • Zhenghong Jin & Qingling Zhang & Xinyou Meng, 2019. "The impulse analysis of the T-S fuzzy singular system via Kronecker index," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(7), pages 1327-1337, May.
    • Handle: RePEc:taf:tsysxx:v:50:y:2019:i:7:p:1327-1337
    DOI: 10.1080/00207721.2019.1587545
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    Cited by:

    1. Liu, Yiqun & Zhuang, Guangming & Zhao, Junsheng & Lu, Junwei & Wang, Zekun, 2023. "H∞.. admissibilization for time-varying delayed nonlinear singular impulsive jump systems based on memory state-feedback control," Applied Mathematics and Computation, Elsevier, vol. 447(C).

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