International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 741–749 | Cite as

Relaxed Stability Conditions for Discrete-Time T–S Fuzzy Systems via Double Homogeneous Polynomial Approach

  • Jun ChenEmail author
  • Shengyuan Xu
  • Qian Ma
  • Guangming Zhuang


This paper deals with the problem of stability analysis for discrete-time Takagi–Sugeno (T–S) fuzzy systems. The double homogeneous polynomially parameter-dependent (DHPPD) Lyapunov function is proposed, which is expressed in the double homogeneous polynomial form not only of the membership functions but also of the state variables. Based on the DHPPD Lyapunov function, a relaxed stability condition is derived. Additionally, the complete square matricial representation of homogeneous polynomials is considered to further reduce the conservatism. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.


Homogeneous polynomials Lyapunov functions Stability Takagi–Sugeno (T–S) fuzzy systems 



This work was supported in part by the National Nature Science Foundation under Grants 61673215, 61403199, 61403178, the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant ZR2016JL025.


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Science and TechnologyNanjingChina
  2. 2.School of Mathematical SciencesLiaocheng UniversityLiaochengChina

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