Delay Dependent Robust Stability of A Discrete Time Recurrent Neural Network with Time Varying Delays

Elizabeth S., Priya P.

Abstract


In this paper, the robust stability analysis of a problem is investigated for a class of discrete recurrent neural networks with distributed time varying delays for delay dependent case. The problem is to determine the robust stability by employing Lyapunov–Krasovskii stability theory. The class of neural network under some consideration is globally asymptotically stable if the quadratic matrix inequality involving several parameters is less than zero. Furthermore, a Linear Matrix Inequality (LMI) approach is provided to show the stability analysis. The numerical examples are given to show the usefulness of the proposed robust stability conditions. The numerical simulation is proved using MATLAB.

Keywords


Delay dependent; Recurrent neural network; Lyapunov–Krasovskii; Linear matrix inequality; Robust stability

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References


B. Zhang, S. Xu and Y. Zou, Improved delay dependent exponential stability criteria for discrete recurrent neural networks with time varying delays, Neurocomputing 72 (2008), 321 – 330.

B. Zhang, S. Xu and Y. Li, Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays, International Journal of Neural Systems 17 (3) (2007), 207 – 218.

C. Hua, C. Long and X. Guan, New results on stability analysis of neural networks with time varying delays, Physics Letters 352 (2006), 335 – 340.

E. Kaslik and St. Balint, Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network, Chaos, Solitons and Fractals 34 (2007), 1245 – 1253.

E. Kaslik and St. Balint, Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections, Chaos, Solitons and Fractals 39 (2009), 83 – 91.

H. Zhang, Z. Wang and D. Liu, Global Asymptotic stability of recurrent neural networks with multiple time-varying delays, IEEE Transactions on Neural Networks 19 (5) (May 2008), 855 – 873.

M.-Z. Luo and S.-M. Zhong, Improved delay-dependent stability criteria for discrete-time stochastic neural networks with time-varying delays, Procedia Engineering 15 (2011), 4456 – 4460.

M. Wu, Y. He, J.-H. She and G.-P. Liu, Delay dependent criteria for robust stability of time varying delay systems, Automatica 40 (2004), 1435 – 1439.

O.M. Kwon, Ju H. Park, S.M. Lee and E.J. Cha, Analysis on delay-dependent stability for neural networks with time-varying delays, Neurocomputing 103 (2013), 114 – 120.

P.-L. Liu, Delay-dependent robust stability analysis for recurrent neural networks with timevarying delay, International Journal of Innovative Computing, Information and Control 9(8) (August 2013), 3341 – 3355.

Q. Yang, Q. Ren and X. Xie, New delay dependent stability criteria for recurrent neural networks with interval time-varying delay, ISA Transactions 53(4) (July 2014), 994 – 999.

S. H. Kim, Further results on stability analysis of discrete-time systems with time-varying delays via the use of novel convex combination coefficients, Applied Mathematics and Computation 261 (2015), 104 – 113.

Y. He, M. Wu and J.-H. She, Delay-dependent exponential stability of delayed neural networks with time-varying delay, IEEE Transaction on Circuits and Systems 53 (7) (July 2006), 553 – 557.

Y. He, Q.G. Wang, C. Lin and M. Wu, Delay range dependent stability for systems with time varying delay, Automatica 43 (2007), 371 – 376.




DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.953

eISSN 0975-5748; pISSN 0974-875X