Exponential state estimation for impulsive neural networks with time delay in the leakage term

Xilin Fu1, Xiaodi Li1, Haydar Akça2
1School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, People’s Republic of China
2Department of Mathematics, College of Arts and Science Faculty, Abu Dhabi University, P.O. Box 59911, Abu Dhabi, United Arab Emirates

Tóm tắt

Từ khóa


Tài liệu tham khảo

Arik S., Tavsanoglu V.: On the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Circ. Syst. I 47, 571–574 (2000)

Arik S.: analysis of exponential stability of delayed neural networks with time varying delays. Neural Networks 17, 1027–1031 (2004)

Bainov D., Simenov P.: Systems with Impulse Effect: Stability Theory and Applications. Ellis Horwood, Chichester (1989)

Baldi P., Atiya A.: How delays affect neural dynamics and learning. IEEE Trans. Neural Networks 5, 612–621 (1994)

Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics. SIAM, Philadelphia (1994)

Cao, J.; Ho, D.; Yang, Y.: Projective synchronization of a class of delayed chaotic systems via impulsive control. Phys. Lett. A 373, 3128–3133 (2009)

Cao, J.; Jiang, Q.: An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays. Phys. Lett. A 330, 203–213 (2004)

Cao, J.; Yuan, K.; Li, H.: Global asymptotic stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Networks 17, 1646–1651 (2006)

Chen, Y.; Bi, W.; Li, W.; Wu, Y.: Less conservative results of state estimation for neural networks with time-varying delay. Neurocomputing 73, 1324–1331 (2010)

Cohen M., Grossberg S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man. Cyber. 13, 815–826 (1983)

Elanayar V., Shin Y.: Approximation and estimation of nonlinear stochastic dynamic systems using radial basis function neural networks. IEEE Trans. Neural Networks 5, 594–603 (1994)

Gopalsamy K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer, Dordrecht (1992)

Gopalsamy K.: Leakage delays in BAM. J. Math. Anal. Appl. 325, 1117–1132 (2007)

Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice-Hall, Englewood Cliffs (1998)

He, Y.; Wang, Q.; Wu, M.; Lin, C.: Delay-dependent state estimation for delayed neural networks. IEEE Trans. Neural Networks 17, 1077–1081 (2006)

He G., Cao Z., Zhu P., Ogura H.: Controlling chaos in a chaotic neural network. Neural Networks 16, 1195–1200 (2003)

Hopfield J.: J Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)

Ji D., Koo J., Won S., Lee S., Park J.: Passivity-based control for Hopfield neural networks using convex representation. Appl. Math. Comput. 217, 6168–6175 (2011)

Kosko B.: Neural Networks and Fuzzy Systems. Prentice Hall, New Delhi (1992)

Kwon O., Park J., Lee S., Cha E.: A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays. Appl. Math. Comput. 217, 10231–10238 (2011)

Lakshmikantham, V.; Bainov, D.; Simeonov, P.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)

Lee, S.; Kwon, O.; Park, J.: A novel delay-dependent criterion for delayed neural networks of neutral type. Phys. Lett. A 374, 1843–1848 (2010)

Li, X.; Chen, Z.: Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Anal. RWA 10, 3253–3265 (2009)

Li, X.; Global exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control. Neurocomputing 73, 525–530 (2009)

Li, T.; Fei, S.: Exponential state estimation for recurrent neural networks with distributed delays. Neurocomputing 71, 428–438 (2007)

Li X.: Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Appl. Math. Comput. 215, 4370–4384 (2010)

Li X., Fu X., Balasubramaniam P., Rakkiyappan R.: Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations. Nonlinear Anal. RWA 11, 4092–4108 (2010)

Liao X., Li C.: An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D 200, 139–155 (2005)

Mahmoud M.: New exponentially convergent state estimation method for delayed neural networks. Neurocomputing 72, 3935–3942 (2009)

Mohamad S., Gopalsamy K., Akca H.: Exponential stability of artificial neural networks with distributed delays and large impulses. Nonlinear Anal. RWA 9, 872–888 (2008)

Niculescu S.: Delay Effects on Stability: A Robust Control Approach. Springer, New York (2001)

Park, J.; Kwon, O.: Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl. Math. Comput. 208, 69–75 (2009)

Park, J.; Kwon, O.: Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202, 360–369 (2008)

Park, J.; Kwon, O.; Lee, S.: State estimation for neural networks of neutral-type with interval time-varying delay. Appl. Math. Comput. 203, 217–223 (2008)

Peng S.: attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal. RWA. 11, 2141–2151 (2010)

Rakkiyappan R., Balasubramaniam P., Lakshmanan S: Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. Phys. Lett. A 372, 5290–5298 (2008)

Song, Q.; Zhang, J.: Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays. Nonlinear Anal. RWA 9, 500–510 (2008)

Wang H., Song Q.: State estimation for neural networks with mixed interval time-varying delays. Neurocomputing 73, 1281–1288 (2010)

Wang Z., Liu Y., Liu X.: On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345, 299–308 (2005)

Wang Z., Ho DWC., Liu X.: State estimation for delayed neural networks. IEEE Trans. Neural Networks 16, 279–284 (2005)

Wang Z., Liu Y., Liu X.: State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Networks 22, 41–48 (2009)

Xia, Y.; Cao, J.; Lin, M.: New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays. Chaos Solit. Fract. 31, 928–936 (2007)

Xia Y., Yang Z., Han M.: Exponential p-stability of delayed CohenCGrossberg-type BAM neural networks with impulses. Chaos Solit. Fract. 38, 806–818 (2008)

Xia Y., Huang Z., Han M.: Existence and globally exponential stability of equilibrium for BAM neural networks with impulses, Chaos Solit. Fract. 37, 588–597 (2008)

Xu D., Yang Z.: Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305, 107–120 (2005)

Xu S., Lam J.: A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Networks 19, 76–83 (2006)