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LMI‐Based Stability Criterion of Impulsive T‐S Fuzzy Dynamic Equations via Fixed Point Theory

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  • Ruofeng Rao
  • Zhilin Pu

Abstract

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI‐based stability criterion of a class of time‐delay Takagi‐Sugeno (T‐S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI‐based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI‐based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Ruofeng Rao & Zhilin Pu, 2013. "LMI‐Based Stability Criterion of Impulsive T‐S Fuzzy Dynamic Equations via Fixed Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:261353
    DOI: 10.1155/2013/261353
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    References listed on IDEAS

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    1. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian‐Jumping Cohen‐Grossberg Neural Networks with Nonlinear p‐Laplace Diffusion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Ruofeng Rao & Xiongrui Wang & Shouming Zhong & Zhilin Pu, 2013. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear -Laplace Diffusion," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-21, May.
    3. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    4. Xianghong Lai & Yutian Zhang, 2012. "Fixed Point and Asymptotic Analysis of Cellular Neural Networks," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Xianghong Lai & Yutian Zhang, 2012. "Fixed Point and Asymptotic Analysis of Cellular Neural Networks," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, August.
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