A New Sufficient Conditions of Stability for Discrete Time Non-autonomous Delayed Hopfield Neural Networks
In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.
[1] M.Wu, Y.He, J.H.She, Stability Analysis and Robust control of Time-
Delay Systems. Springer Heidelberg Dordrecht London New York (2010)
21-22.
[2] Q.Zhang, X.P.Wei, J.Xu, Global exponential stability for nonautonomous
cellular neural networks with delays. Phys. Lett. A 351 (2006) 153-160.
[3] Q.Zhang, X.P.Wei, J.Xu, Stability of delayed cellular neural networks.
Chaos Solitons Fractals 31 (2007) 514-520.
[4] Q.Zhang, X.P.Wei, J.Xu, Delay-Dependent global stability condition for
delayed Hopfield neural networks. Nonlinear Anal. RWA 8(2007)997-
1002.
[5] Q.Zhang, X.P.Wei, J.Xu, A new global stability result for delayed neural
networks. Nonlinear Anal. RWA 8 (2007)1024-1028.
[6] J.Zhang, X.Jin, Global stability analysis in delayed Hopfield neural
network models, Neural Networks 13 (2000)745-753.
[7] Z.Chen, J.Ruan, Physics Letters A 345(2005)101.
[8] B.Liu, X.Z.Liu, X.X.Liao, Control Theory and Applications 19 (2) (2003)
168.
[9] H.G.Zhang, G.Wang, Neurocomputing 70 (2007)2486.
[10] S.Mohamed, K.Gopalsamy, Exponential stability of continuous-time and
discrete-time cellular neural networks with delays. Appl.Math.Comput.
135(2003)17-38.
[11] Y.liu, Z.Wang, A.Serrano, X.Liu, Discrete-time recurrent neural networks
with time-varying delays: Exponential analysis. Phys.Lett. A
362(2007)480-488.
[12] Q.Zhang, X.P.Wei, J.Xu, A novel global exponential stability result
for disrete-time cellular neural networks with variable delays. Internat.
J.Neural Syst. 16 (2006)467-472.
[13] W.H.Chen, X.Lu, D.Y.Liang, Global exponential stability for discretetime
neural networks with variable delays, Phys.Lett.A358(2006)186-198.
[14] J.Liang, J.Cao, J.Lam, Convergence of discrete-time recurrent neural
networks with variable delay. Internat, J.Bifur.Chaos 15(2005)581-595.
[15] S.Mohamad, K.Gopalsamy, Dynamics of a class of discrete-time neural
networks and their continuous-time counterparts. Math.Comput.Simul. 53
(2000)1-39.
[16] X.Wei, D.Zhou, Q.Zhang, On asymptotic stability of disrete-time nonautonomous
delayed Hopfield neural networks. Computer and Mathematics
with Applications 57 (2009)1938-1942.
[17] A.Berman, R.J.Plemmons, Nonnegative Matrices in Mathematical Sciences.
Academic Press, New York, 1979.
[1] M.Wu, Y.He, J.H.She, Stability Analysis and Robust control of Time-
Delay Systems. Springer Heidelberg Dordrecht London New York (2010)
21-22.
[2] Q.Zhang, X.P.Wei, J.Xu, Global exponential stability for nonautonomous
cellular neural networks with delays. Phys. Lett. A 351 (2006) 153-160.
[3] Q.Zhang, X.P.Wei, J.Xu, Stability of delayed cellular neural networks.
Chaos Solitons Fractals 31 (2007) 514-520.
[4] Q.Zhang, X.P.Wei, J.Xu, Delay-Dependent global stability condition for
delayed Hopfield neural networks. Nonlinear Anal. RWA 8(2007)997-
1002.
[5] Q.Zhang, X.P.Wei, J.Xu, A new global stability result for delayed neural
networks. Nonlinear Anal. RWA 8 (2007)1024-1028.
[6] J.Zhang, X.Jin, Global stability analysis in delayed Hopfield neural
network models, Neural Networks 13 (2000)745-753.
[7] Z.Chen, J.Ruan, Physics Letters A 345(2005)101.
[8] B.Liu, X.Z.Liu, X.X.Liao, Control Theory and Applications 19 (2) (2003)
168.
[9] H.G.Zhang, G.Wang, Neurocomputing 70 (2007)2486.
[10] S.Mohamed, K.Gopalsamy, Exponential stability of continuous-time and
discrete-time cellular neural networks with delays. Appl.Math.Comput.
135(2003)17-38.
[11] Y.liu, Z.Wang, A.Serrano, X.Liu, Discrete-time recurrent neural networks
with time-varying delays: Exponential analysis. Phys.Lett. A
362(2007)480-488.
[12] Q.Zhang, X.P.Wei, J.Xu, A novel global exponential stability result
for disrete-time cellular neural networks with variable delays. Internat.
J.Neural Syst. 16 (2006)467-472.
[13] W.H.Chen, X.Lu, D.Y.Liang, Global exponential stability for discretetime
neural networks with variable delays, Phys.Lett.A358(2006)186-198.
[14] J.Liang, J.Cao, J.Lam, Convergence of discrete-time recurrent neural
networks with variable delay. Internat, J.Bifur.Chaos 15(2005)581-595.
[15] S.Mohamad, K.Gopalsamy, Dynamics of a class of discrete-time neural
networks and their continuous-time counterparts. Math.Comput.Simul. 53
(2000)1-39.
[16] X.Wei, D.Zhou, Q.Zhang, On asymptotic stability of disrete-time nonautonomous
delayed Hopfield neural networks. Computer and Mathematics
with Applications 57 (2009)1938-1942.
[17] A.Berman, R.J.Plemmons, Nonnegative Matrices in Mathematical Sciences.
Academic Press, New York, 1979.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50302", author = "Adnene Arbi and Chaouki Aouiti and Abderrahmane Touati", title = "A New Sufficient Conditions of Stability for Discrete Time Non-autonomous Delayed Hopfield Neural Networks", abstract = "In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.
", keywords = "Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.", volume = "6", number = "3", pages = "209-6", }
