Finite-time extended dissipativity of delayed Takagi–Sugeno fuzzy neural networks using a free-matrix-based double integral inequality

Abstract

This study focuses on the finite-time extended dissipativity of delayed Takagi–Sugeno (T–S) fuzzy neural networks (NNs). Based on the concept of extended dissipativity, this paper solves the \(H_\infty\), \(L_2-L_\infty\), passive, and \(({{\mathcal {Q}}}, {{\mathcal {S}}}, {\mathcal {R}})\)-dissipativity performance in a unified framework. Using the free-matrix-based double integral inequality and an extended Wirtinger inequality in the Lyapunov–Krasovskii functional, sufficient conditions are derived to guarantee that the considered NNs are finite-time bounded, whereupon the finite-time extended dissipativity criteria for delayed T–S fuzzy NNs are constructed. The derived conditions guarantee the extended dissipativity and stability of the NNs. Three numerical examples are given to demonstrate the reduced conservatism and the effectiveness of the obtained results.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIT) (No. 2018R1A2B3008890)

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Correspondence to Gyu M. Lee.

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Shanmugam, S., Muhammed, S.A. & Lee, G.M. Finite-time extended dissipativity of delayed Takagi–Sugeno fuzzy neural networks using a free-matrix-based double integral inequality. Neural Comput & Applic 32, 8517–8528 (2020). https://doi.org/10.1007/s00521-019-04348-w

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Keywords

  • Extended dissipativity
  • Extended Wirtinger inequality
  • Finite-time bounded
  • Free-weighting matrix
  • Lyapunov–Krasovskii functional
  • Takagi–Sugeno fuzzy neural networks