Improved Robust Stability Criteria for Discrete-time Neural Networks
In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080237Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1132
 Y. He, et al., Stability analysis for neural networks with time-varying interval delay, IEEE Trans. Neural Netw., 18 (2007) 1850-1854.
 J. Qiu, J. Cao, Delay-dependent exponential stability for a class of neural networks with time delays and reactionCdiffusion terms, J. Franklin Inst., 4 (2009) 301-314.
 J. Wang, L. Huang and Z. Guo, Dynamical behavior of delayed Hopfield neural networks with discontinuous activations, Appl. Math. Model., 33 (2009) 1793-1802.
 Y. Xia, Z. Huang and M. Han, Exponential p-stability of delayed Cohen- Grossberg-type BAM neural networks with impulses, Chaos, Solitons and Fractals, 38 (2008) 806-818.
 Y, Liu, Z, Wang and X, Liu, Asymptotic stability for neural networks with mixed time-delays: The discrete-time case, Neural Networks, 22 (2009) 67-74.
 Z. Han, W. Li, Global stability analysis of interval neural networks with discrete and distributed delays of neutral type, Exp. Syst. Appl., 36 (2009) 7328-7331.
 O. Kwon, J. Park, Improved delay-dependent stability criterion for neural networks with time-varying delays, Phys. Lett. A., 373 (2009) 529-535.
 Y. Liu, Z. Wang and X. Liu, Robust stability of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, 71 (2008) 823-833.
 M. Ali, P. Balasubramaniam, Stability analysis of uncertain fuzzy Hopfield neural networks with time delays, Commun. Nonlinear Sci. Numer. Simulat., 14 (2009) 2776-2783.
 W. Xiong, L. Song and J. Cao, Adaptive robust convergence of neural networks with time-varying delays, Nonlinear Anal: Real. world. Appl., 9 (2008) 1283-1291.
 W. Yu, L. Yao, Global robust stability of neural networks with time varying delays, J. Comput. Appl. Math., 206 (2007) 679- 687.
 H. Cho, J. Park, Novel delay-dependent robust stability criterion of delayed cellular neural networks, Chaos, Solitons and Fractals, 32 (2007) 1194-1200.
 Q. Song, J. Cao, Global robust stability of interval neural networks with multiple time-varying delays, Math. Comput. Simulat., 74 (2007) 38-46.
 T. Li, L. Guo and C. Sun, Robust stability for neural networks with timevarying delays and linear fractional uncertainties, Neurocomputing, 71 (2007) 421-427.
 W. Feng, et al., Robust stability analysis of uncertain stochastic neural networks with interval time-varying delay, Chaos, Solitons and Fractals, 1 (2009), 414-424.
 Z. Wu, et al., New results on robust exponential stability for discrete recurrent neural networks with time-varying delays, Neurocomputing, 72 (2009), 3337-3342.
 M. Luo, et al., Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays, Appl. Math. Comput., 2 (2009) 305-313.
 J. Liang, et al., Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks, IEEE Trans. Neural Netw., 19 (2008) 1910-1920.
 V. Singh, Improved global robust stability of interval delayed neural networks via split interval: Generalizations, Appl. Math. Comput., 206 (2008) 290-297.
 K. Patan, Stability Analysis and the Stabilization of a Class of Discrete- Time Dynamic Neural Networks, IEEE Trans. Neural Netw., 18 (2007) 660-672.
 Q. Song, Z. Wang, A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays, Phys. Lett. A., 368 (2007) 134-145.
 B. Zhang, S. Xu and Y. Zou, Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with timevarying delays, Neurocomputing, 72 (2008) 321-330.
 J. Yu, K. Zhang, S. Fei, Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay, Nonlinear Analysis: Real World Applications (2008), doi:10.1016/j.nonrwa.2008.10.053
 Y. Zhang, S. Xu and Z. Zeng, Novel robust stability criteria of discretetime stochastic recurrent neural networks with time delay, Neurocomputing, 13 (2009), 3343-3351.
 X. Liu, et al., Discrete-time BAM neural networks with variable delays, Phys. Lett. A., 367 (2007) 322-330.
 H. Zhao, L. Wang and C. Ma, Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay, Nonlinear Anal: Real World Appl., 9 (2008) 103-113.
 H. Gao, T. Chen, New results on stability of discrete-time systems with time-varying state delay, IEEE Trans. Autom. Control., 52 (2007) 328- 334.
 Y. Liu, et al., Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis, Phys. Lett. A., 362 (2007) 480-488.
 C. Song, et al., A new approach to stability analysis of discrete-time recurrent neural networks withtime-varyingdelay, Neurocomputing, 10 (2009) 2563-2568.
 T. Lee, U. Radovic, General decentralized stabilization of large-scale linear continuous and discrete time-delay systems, Inter. Jour.Cont., 46 (1987) 2127-2140.
 L. Xie, Output feedback H1 control of systems with parameter uncertainty, Int.J. Control., 63 (1996) 741-50.
 S. Boyd, et al., Linear matrix inequalities in systems and control theory, Philadelphia (PA): SIAM, 1994.