Exponential Stability of Uncertain Takagi-Sugeno Fuzzy Hopfield Neural Networks with Time Delays

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.

Keywords: Hopfield neural network, linear matrix inequality, exponential stability, time delay, T-S fuzzy model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057585

References:

[1] J. Hopfield, Neural networks and physical systems with emergent collect computational abilities. Proc. Natl. Acad. Sci. USA; 1982; 2554-2558 .
[2] J. Hopfield, Neurons with graded response have collective computational proporties like those of two-state neurons. Proc. Natl. Acad. Sci. USA; 1984; 3088-3092.
[3] S. Chen, Q. Zhang, C. Wang, Existence and stability of equilibria of the continuous-time Hopfield neural network. Journal of Computational and Applied Mathematics 2004; 169; 117-125.
[4] S. Hu, X. Liao, X. Mao, Stochastic Hopfield neural networks. J. Phys. A: Math. Gen. 2004; 9; 47-53.
[5] H. Huang, D. Ho, J. Lam, Stochastic stability analysis of fuzzy Hopfield neural networks with Time-Varying Delays. IEEE Trans. Circuits Syst. II, Exp. Briefs 2005; 52; 251- 255.
[6] Z. Wang, H. Shu, J. Fang, X. Liu. Robust stability for stochastic Hopfield neurarl networks with time delays. Nonlinear Anal. Real World. Appl. 2006, 7: 1119-1128.
[7] X. Mao, N. Koroleva, A. Rodkina, Robust stability of uncertain stochastic delay differential equations. Systems Control lett. 1998; 35; 325-336.
[8] K. Tanaka, T. Ikede, H. Wang, Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H control theory, andlinear matrix inequalities. IEEE Trans. Fuzzy Systems 1996; 4; 1-13.
[9] Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time delays. Chaos Solitons Fractals 2007; 32; 62-72.
[10] Z. Wang, H. Qiao, Robust filtering for bilinear uncertain stochastic discrete-time systems. IEEE Trans. Signal Process. 2002; 50(3); 560-567.
[11] T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man, Cybern. 1985; 15; 116 - 132.
[12] Y. Cao, P. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models. Fuzzy Sets and Systems 2001; 124; 213-229.
[13] T. Takagi, M. Sugeno, Stability analysis andd esign of fuzzy control systems. Fuzzy Sets and Systems 1993; 45; 135-156.
[14] K. Tanaka, T. Ikede, H. Wang, An LMI approach to fuzzy controller designs basedon the relaxed stability conditions Proceedings of the IEEE international conference on fuzzy systems. Barcelona Spain; 1997; 171- 176.
[15] K. Tanaka, T. Ikede, H. Wang, Fuzzy regulators and fuzzy observers: Relaxedstability conditions and LMI-based design. IEEE Trans. Fuzzy Systems 1998; 6; 250-265.
[16] P. Gahinet, Nemirovski A, Laub A, Chilali M. LMI control toolbox user-s guide. The Mathworks; Massachusetts; 1995.
[17] B. Boyd, L. Ghoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM; philadephia; 1994.
[18] H. Zhao, Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Networks. 2004; 17; 4753.
[19] L. Xie, Output feedback H control of systems with parameter uncertainty. Internat. J. control 1996; 63; 741-759.
[20] K. Gu, V. Kharitonov, J. Chen, Stability of time delay systems. Birkhuser; Boston; 2003.