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.
[1] Y. He, et al., Stability analysis for neural networks with time-varying
interval delay, IEEE Trans. Neural Netw., 18 (2007) 1850-1854.
[2] 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.
[3] J. Wang, L. Huang and Z. Guo, Dynamical behavior of delayed Hopfield
neural networks with discontinuous activations, Appl. Math. Model., 33
(2009) 1793-1802.
[4] 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.
[5] 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.
[6] 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.
[7] O. Kwon, J. Park, Improved delay-dependent stability criterion for neural
networks with time-varying delays, Phys. Lett. A., 373 (2009) 529-535.
[8] Y. Liu, Z. Wang and X. Liu, Robust stability of discrete-time stochastic
neural networks with time-varying delays, Neurocomputing, 71 (2008)
823-833.
[9] M. Ali, P. Balasubramaniam, Stability analysis of uncertain fuzzy Hopfield
neural networks with time delays, Commun. Nonlinear Sci. Numer.
Simulat., 14 (2009) 2776-2783.
[10] 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.
[11] W. Yu, L. Yao, Global robust stability of neural networks with time
varying delays, J. Comput. Appl. Math., 206 (2007) 679- 687.
[12] H. Cho, J. Park, Novel delay-dependent robust stability criterion of
delayed cellular neural networks, Chaos, Solitons and Fractals, 32 (2007)
1194-1200.
[13] Q. Song, J. Cao, Global robust stability of interval neural networks with
multiple time-varying delays, Math. Comput. Simulat., 74 (2007) 38-46.
[14] T. Li, L. Guo and C. Sun, Robust stability for neural networks with timevarying
delays and linear fractional uncertainties, Neurocomputing, 71
(2007) 421-427.
[15] 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.
[16] Z. Wu, et al., New results on robust exponential stability for discrete
recurrent neural networks with time-varying delays, Neurocomputing, 72
(2009), 3337-3342.
[17] 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.
[18] 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.
[19] V. Singh, Improved global robust stability of interval delayed neural
networks via split interval: Generalizations, Appl. Math. Comput., 206
(2008) 290-297.
[20] K. Patan, Stability Analysis and the Stabilization of a Class of Discrete-
Time Dynamic Neural Networks, IEEE Trans. Neural Netw., 18 (2007)
660-672.
[21] 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.
[22] 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.
[23] 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
[24] 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.
[25] X. Liu, et al., Discrete-time BAM neural networks with variable delays,
Phys. Lett. A., 367 (2007) 322-330.
[26] 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.
[27] 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.
[28] Y. Liu, et al., Discrete-time recurrent neural networks with time-varying
delays: Exponential stability analysis, Phys. Lett. A., 362 (2007) 480-488.
[29] C. Song, et al., A new approach to stability analysis of discrete-time
recurrent neural networks withtime-varyingdelay, Neurocomputing, 10
(2009) 2563-2568.
[30] T. Lee, U. Radovic, General decentralized stabilization of large-scale
linear continuous and discrete time-delay systems, Inter. Jour.Cont., 46
(1987) 2127-2140.
[31] L. Xie, Output feedback H1 control of systems with parameter uncertainty,
Int.J. Control., 63 (1996) 741-50.
[32] S. Boyd, et al., Linear matrix inequalities in systems and control theory,
Philadelphia (PA): SIAM, 1994.
[1] Y. He, et al., Stability analysis for neural networks with time-varying
interval delay, IEEE Trans. Neural Netw., 18 (2007) 1850-1854.
[2] 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.
[3] J. Wang, L. Huang and Z. Guo, Dynamical behavior of delayed Hopfield
neural networks with discontinuous activations, Appl. Math. Model., 33
(2009) 1793-1802.
[4] 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.
[5] 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.
[6] 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.
[7] O. Kwon, J. Park, Improved delay-dependent stability criterion for neural
networks with time-varying delays, Phys. Lett. A., 373 (2009) 529-535.
[8] Y. Liu, Z. Wang and X. Liu, Robust stability of discrete-time stochastic
neural networks with time-varying delays, Neurocomputing, 71 (2008)
823-833.
[9] M. Ali, P. Balasubramaniam, Stability analysis of uncertain fuzzy Hopfield
neural networks with time delays, Commun. Nonlinear Sci. Numer.
Simulat., 14 (2009) 2776-2783.
[10] 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.
[11] W. Yu, L. Yao, Global robust stability of neural networks with time
varying delays, J. Comput. Appl. Math., 206 (2007) 679- 687.
[12] H. Cho, J. Park, Novel delay-dependent robust stability criterion of
delayed cellular neural networks, Chaos, Solitons and Fractals, 32 (2007)
1194-1200.
[13] Q. Song, J. Cao, Global robust stability of interval neural networks with
multiple time-varying delays, Math. Comput. Simulat., 74 (2007) 38-46.
[14] T. Li, L. Guo and C. Sun, Robust stability for neural networks with timevarying
delays and linear fractional uncertainties, Neurocomputing, 71
(2007) 421-427.
[15] 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.
[16] Z. Wu, et al., New results on robust exponential stability for discrete
recurrent neural networks with time-varying delays, Neurocomputing, 72
(2009), 3337-3342.
[17] 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.
[18] 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.
[19] V. Singh, Improved global robust stability of interval delayed neural
networks via split interval: Generalizations, Appl. Math. Comput., 206
(2008) 290-297.
[20] K. Patan, Stability Analysis and the Stabilization of a Class of Discrete-
Time Dynamic Neural Networks, IEEE Trans. Neural Netw., 18 (2007)
660-672.
[21] 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.
[22] 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.
[23] 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
[24] 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.
[25] X. Liu, et al., Discrete-time BAM neural networks with variable delays,
Phys. Lett. A., 367 (2007) 322-330.
[26] 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.
[27] 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.
[28] Y. Liu, et al., Discrete-time recurrent neural networks with time-varying
delays: Exponential stability analysis, Phys. Lett. A., 362 (2007) 480-488.
[29] C. Song, et al., A new approach to stability analysis of discrete-time
recurrent neural networks withtime-varyingdelay, Neurocomputing, 10
(2009) 2563-2568.
[30] T. Lee, U. Radovic, General decentralized stabilization of large-scale
linear continuous and discrete time-delay systems, Inter. Jour.Cont., 46
(1987) 2127-2140.
[31] L. Xie, Output feedback H1 control of systems with parameter uncertainty,
Int.J. Control., 63 (1996) 741-50.
[32] S. Boyd, et al., Linear matrix inequalities in systems and control theory,
Philadelphia (PA): SIAM, 1994.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61987", author = "Zixin Liu and Shu Lü and Shouming Zhong and Mao Ye", title = "Improved Robust Stability Criteria for Discrete-time Neural Networks", abstract = "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.
", keywords = "Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.", volume = "4", number = "7", pages = "1007-6", }
