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2013 | 23 | 1 | 201-211

Tytuł artykułu

Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous results. Finally, two numerical examples are given to illustrate the advantages of the obtained results.

Rocznik

Tom

23

Numer

1

Strony

201-211

Opis fizyczny

Daty

wydano
2013
otrzymano
2011-12-31
poprawiono
2012-05-09

Twórcy

autor
  • College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
  • College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
autor
  • Department of Mathematics, Southeast University, Nanjing 210096, China
autor
  • College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
  • Academic Affairs Division, Zhejiang Normal University, Jinhua 321004, China
autor
  • College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China

Bibliografia

  • Ahmad, S. and Stamova, I. (2008). Global exponential stability for impulsive cellular neural networks with time-varying delays, Nonlinear Analysis: Theory, Methods & Applications 69(3): 786-795.
  • Cao, J. and Xiao, M. (2007). Stability and Hopf bifurcation in a simplified BAM neural network with two time delays, IEEE Transactions on Neural Networks 18(2): 416-430.
  • Chen, T. (2001). Global exponential stability of delayed Hopfield neural networks, Neural Networks 14(8): 977-980.
  • Chua, L. and Yang, L. (1988a). Cellular neural networks: Applications, IEEE Transactions on Circuits and Systems 35(10): 1273-1290.
  • Chua, L. and Yang, L. (1988b). Cellular neural networks: Theory, IEEE Transactions on Circuits and Systems 35(10): 1257-1272.
  • Civalleri, P., Gilli, M. and Pandolfi, L. (1993). On stability of cellular neural networks with delay, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 40(3): 157-165.
  • Gopalsamy, K. and He, X. (1994). Stability in asymmetric Hopfield nets with transmission delays, Physica D: Nonlinear Phenomena 76(4): 344-358.
  • Halanay, A. (1966). Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, NY.
  • He, Y., Wang, Q., Wu, M. and Lin, C. (2006). Delay-dependent state estimation for delayed neural networks, IEEE Transactions on Neural Networks 17(4): 1077-1081.
  • Ho, D., Liang, J. and Lam, J. (2006). Global exponential stability of impulsive high-order BAM neural networks with time-varying delays, Neural Networks 19(10): 1581-1590.
  • Huang, Z. and Yang, Q. (2010). Exponential stability of impulsive high-order cellular neural networks with time-varying delays, Nonlinear Analysis: Real World Applications 11(1): 592-600.
  • Khadra, A., Liu, X. and Shen, X. (2009). Analyzing the robustness of impulsive synchronization coupled by linear delayed impulses, IEEE Transactions on Automatic Control 54(4): 923-928.
  • Li, C., Feng, G. and Huang, T. (2008). On hybrid impulsive and switching neural networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38(6): 1549-1560.
  • Li, X. (2010). Global exponential stability of delay neural networks with impulsive perturbations, Advances in Dynamical Systems and Applications 5(1): 107-122.
  • Liu, X., Shen, X., Zhang, Y. and Wang, Q. (2007). Stability criteria for impulsive systems with time delay and unstable system matrices, IEEE Transactions on Circuits and Systems I: Regular Papers 54(10): 2288-2298.
  • Liu, X., Teo, K. and Xu, B. (2005). Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays, IEEE Transactions on Neural Networks 16(6): 1329-1339.
  • Liu, X. and Wang, Q. (2008). Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays, IEEE Transactions on Neural Networks 19(1): 71-79.
  • Liu, Y., Zhao, S. and Lu, J. (2011). A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model, IEEE Transactions on Fuzzy Systems 19(2): 393-398.
  • Lou, X. and Cui, B. (2007). Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays, Journal of Mathematical Analysis and Applications 330(1): 144-158.
  • Lu, J., Ho, D. and Cao, J. (2010). A unified synchronization criterion for impulsive dynamical networks, Automatica 46(7): 1215-1221.
  • Lu, J., Ho, D., Cao, J. and Kurths, J. (2011). Exponential synchronization of linearly coupled neural networks with impulsive disturbances, IEEE Transactions on Neural Networks 22(2): 329-336.
  • Lu, J., Kurths, J., Cao, J., Mahdavi, N. and Huang, C. (2012). Synchronization control for nonlinear stochastic dynamical networks: Pinning impulsive strategy, IEEE Transactions on Neural Networks and Learning Systems 23(2): 285-292.
  • Raja, R., Sakthivel, R., Anthoni, S.M. and Kim, H. (2011). Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays, International Journal of Applied Mathematics and Computer Science 21(1): 127-135, DOI: 10.2478/v10006-011-0009-y.
  • Ren, F. and Cao, J. (2006). LMI-based criteria for stability of high-order neural networks with time-varying delay, Nonlinear Analysis: Real World Applications 7(5): 967-979.
  • Rong, L. (2005). LMI approach for global periodicity of neural networks with time-varying delays, IEEE Transactions on Circuits and Systems I: Regular Papers 52(7): 1451-1458.
  • Sakthivel, R., Raja, R. and Anthoni, S. (2011). Exponential stability for delayed stochastic bidirectional associative memory neural networks with markovian jumping and impulses, Journal of Optimization Theory and Applications 150(1): 166-187.
  • Sakthivel, R., Samidurai, R. and Anthoni, S. (2010a). Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects, Journal of Optimization Theory and Applications 147(3): 583-596.
  • Sakthivel, R., Samidurai, R. and Anthoni, S. (2010b). Exponential stability for stochastic neural networks of neutral type with impulsive effects, Modern Physics Letters B 24(11): 1099-1110.
  • Sakthivel, R., Raja, R. and Anthoni, S. (2010c). Asymptotic stability of delayed stochastic genetic regulatory networks with impulses, Physica Scripta 82(5): 055009.
  • Stamova, I. and Ilarionov, R. (2010). On global exponential stability for impulsive cellular neural networks with time-varying delays, Computers & Mathematics with Applications 59(11): 3508-3515.
  • Stamova, I., Ilarionov, R. and Vaneva, R. (2010). Impulsive control for a class of neural networks with bounded and unbounded delays, Applied Mathematics and Computation 216(1): 285-290.
  • Tian, Y., Yu, X. and Chua, L. (2004). Time-delayed impulsive control of chaotic hybrid systems, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 14(3): 1091-1104.
  • van den Driessche, P. and Zou, X. (1998). Global attractivity in delayed Hopfield neural network models, SIAM Journal on Applied Mathematics 58(6): 1878-1890.
  • Wallis, G. (2005). Stability criteria for unsupervised temporal association networks, IEEE Transactions on Neural Networks 16(2): 301-311.
  • Wang, Q. and Liu, X. (2007). Exponential stability of impulsive cellular neural networks with time delay via Lyapunov functionals, Applied Mathematics and Computation 194(1): 186-198.
  • Weng, A. and Sun, J. (2009). Impulsive stabilization of second-order nonlinear delay differential systems, Applied Mathematics and Computation 214(1): 95-101.
  • Wu, B., Liu, Y. and Lu, J. (2011). Impulsive control of chaotic systems and its applications in synchronization, Chinese Physics B 20(5): 050508.
  • Wu, B., Liu, Y. and Lu, J. (2012a). New results on global exponential stability for impulsive cellular neural networks with any bounded time-varying delays, Mathematical and Computer Modelling 55(3-4): 837-843.
  • Wu, B., Han, J. and Cai, X. (2012b). On the practical stability of impulsive differential equations with infinite delay in terms of two measures, Abstract and Applied Analysis 2012: 434137.
  • Xu, B., Liu, X. and Liao, X. (2003). Global asymptotic stability of high-order hopfield type neural networks with time delays, Computers & Mathematics with Applications 45(10-11): 1729-1737.
  • Xu, B., Liu, X. and Teo, K. (2009). Asymptotic stability of impulsive high-order hopfield type neural networks, Computers & Mathematics with Applications 57(11-12): 1968-1977.
  • Xu, B., Xu, Y. and He, L. (2011). LMI-based stability analysis of impulsive high-order Hopfield-type neural networks, Mathematics and Computers in Simulation, DOI: 10.1016/j.matcom.2011.02.008.
  • Yang, T. and Chua, L. (1997). Impulsive stabilization for control and synchronization of chaotic systems: Theory and application to secure communication, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44(10): 976-988.
  • Yang, Z. and Xu, D. (2005). Stability analysis of delay neural networks with impulsive effects, IEEE Transactions on Circuits and Systems II: Express Briefs 52(8): 517-521.
  • Yang, Z. and Xu, D. (2007). Stability analysis and design of impulsive control systems with time delay, IEEE Transactions on Automatic Control 52(8): 1448-1454.
  • Yue, D., Xu, S. and Liu, Y. (1999). Differential inequality with delay and impulse and its applications to design robust control, Journal of Control Theory and Applications 16(4): 519-524.
  • Zhang, H., Ma, T., Huang, G. and Wang, Z. (2010). Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40(3): 831-844.
  • Zhang, Q., Yang, L. and Liao, D. (2011). Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays, International Journal of Applied Mathematics and Computer Science 21(4): 649-658, DOI: 10.2478/v10006-011-0051-9.
  • Zhang, Y. and Sun, J. (2010). Stability of impulsive linear hybrid systems with time delay, Journal of Systems Science and Complexity 23(4): 738-747.
  • Zheng, C., Zhang, H. and Wang, Z. (2011). Novel exponential stability criteria of high-order neural networks with time-varying delays, IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics 41(2): 486-496.
  • Zhou, J. and Wu, Q. (2009). Exponential stability of impulsive delayed linear differential equations, IEEE Transactions on Circuits and Systems II: Express Briefs 56(9): 744-748.

Typ dokumentu

Bibliografia

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