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Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure

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Abstract

In this paper, based on switched systems and recurrent neural networks (RNNs) with time-varying delay, the model of switched RNNs is formulated. Global asymptotical stability (GAS) and global robust stability (GRS) for such switched neural networks are studied by employing nonlinear measure and linear matrix inequality (LMI) techniques. Some new sufficient conditions are obtained to ensure GAS or GRS of the unique equilibrium of the proposed switched system. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, three examples are provided to illustrate the usefulness of the results.

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References

  1. Arik, S.: Global asymptotic stability of a larger class of neural networks with constant time delay. Phys. Lett. A 311, 504–511 (2003)

    Article  MATH  Google Scholar 

  2. Boyd, S., EI Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadephia (1994)

  3. Cao, J., Wang, J.: Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst.-I 50(1), 34–44 (2003)

    Google Scholar 

  4. Cao, J., Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst.-I 52(2), 417–426 (2005)

    Article  MathSciNet  Google Scholar 

  5. Cheng, D., Guo, L., Lin, Y., Wang, Y.: Stabilization of switched linear systems. IEEE Trans. Autom. Cont. 50(5), 661–666 (2005)

    Article  MathSciNet  Google Scholar 

  6. Daafouz, J., Riedinger, P., Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Cont. 47(11), 1883–1887 (2002)

    Article  MathSciNet  Google Scholar 

  7. Ensari, T., Arik, S.: Global stability of a class of neural networks with time-varying delay. IEEE Trans. Circuits Syst.-II 52(3), 126–130 (2005)

    Google Scholar 

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

    Google Scholar 

  9. Huang, H., Qu, Y., Li, H.: Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty. Phys. Lett. A 345, 345–354 (2005)

    Article  Google Scholar 

  10. Joy, M.: On the global convergence of a class of functional differential equations with applications in neural network theory. J. Math. Anal. Appl. 232, 61–81 (1999)

    Google Scholar 

  11. Lee, S.H., Kim, T.H., Lim, J.T.: A new stability analysis of switched systems. Automatica 36, 917–922 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Li, P., Cao, J.: Stability in static delayed neural networks: a nonlinear measure approach. Neurocomputing 69, 1776–1781 (2006)

    Article  Google Scholar 

  13. Liao, X., Chen, G., Sanchez, E.N.: LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. Circuits Syst.-I 49(7), 1033–1039 (2002)

    Google Scholar 

  14. Liao, X., Wong, K.W., Wu, Z., Chen, G.: Novel robust stability criteria for interval-delayed Hopfield neural networks. IEEE Trans. Circuits Syst.-I 48(11), 1355–1359 (2001)

    Google Scholar 

  15. Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19(5), 59–70 (1999)

    Article  Google Scholar 

  16. Marcus, C.M., Westerveld, R.M.: Stability of analogy neural networks with delay. Phys. Rev. A, 39, 347–359 (1989)

    Article  Google Scholar 

  17. Morita, M.: Associative memory with nonmonotone dynamics. Neural Network, 6, 115–126 (1993)

    Google Scholar 

  18. Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)

  19. Persis, C.D., Santis, R.D., Morse, A.S.: Switched nonlinear systems with state-dependent dwell-time. Syst. Control Lett. 50, 291–302 (2003)

    Google Scholar 

  20. Sanchez, E.N., Perez, J.P.: Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Trans. Circuits Syst.-I 46(11), 1395–1398 (1999)

    Google Scholar 

  21. Skafidas, E., Evans, R.J., Savkin, A.V., Petersen, I.R.: Stability results for switched controller systems. Automatica 35, 553–564 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  22. Xia, Y., Wang, J.: On the stability of globally projected dynamical systems. J. Optim. Theory Appl. 106(1), 129–150 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Xie, G., Wang, L.: Stability of switched linear systems with time-delay in detection of switching signal. J. Math. Anal. Appl. 305, 277–290 (2005)

    Google Scholar 

  24. Xu, S., Lam, J., Ho, D.W.C., Zou, Y.: Improved global robust asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Syst. Man, Cybe.-B 35(6), 1263–1267 (2005)

    Google Scholar 

  25. Xu, S., Lam, J., Ho, D.W.C., Zou, Y.: Novel global asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Circuits Syst.-II 52(6), 349–353 (2005)

    Google Scholar 

  26. Ye, H., Michel, A.N., Hou, L.: Stability theory for hybrid dynamical systems. IEEE Trans. Autom. Control 43(4), 461–474 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  27. Ye, H., Michel, A.N.: Robust stability of nonlinear time-delay systems with applications to neural networks. IEEE Trans. Circuits Syst.-I 43(7), 532–543 (1996)

    Google Scholar 

  28. Zhang, J.: Global stability analysis in delayed cellular neural networks. Comp. Math. Appl. 45, 1707–1720 (2003)

    Google Scholar 

  29. Cao, J., Yuan, K., Li, H.: Global asymptotical stability of generalized recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Networks 17(6), 1646–1651 (2006)

    Google Scholar 

  30. Cao, J., Song, Q.: Stability in Cohen-Grossberg type BAM neural networks with time-varying delays. Nonlinearity 19(7), 1601–1617 (2006)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Ping Li & Jinde Cao

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  1. Ping Li
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  2. Jinde Cao
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Correspondence to Jinde Cao.

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Li, P., Cao, J. Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure. Nonlinear Dyn 49, 295–305 (2007). https://doi.org/10.1007/s11071-006-9134-9

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  • DOI: https://doi.org/10.1007/s11071-006-9134-9

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