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Exponential stability for switched Cohen–Grossberg neural networks with average dwell time

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Abstract

In this paper, uncertain switched Cohen–Grossberg neural networks with interval time-varying delay and distributed time-varying delay are proposed. Novel multiple Lyapunov functions are employed to investigate the stability of the switched neural networks under the switching rule with the average dwell time property. Sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) which guarantee the exponential stability for the switched Cohen–Grossberg neural networks. Numerical examples are provided to illustrate the effectiveness of the proposed method.

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References

  1. Lu, K., Xu, D., Yang, Z.: Global attraction and stability for Cohen–Grossberg neural networks with delays. Neural Netw. 19(10), 1538–1549 (2006)

    Article  MATH  Google Scholar 

  2. Cohen, M.A., Grossberg, S.: Absolute stability of global pattern formulation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. SMC-13, 815–826 (1983)

    MathSciNet  Google Scholar 

  3. Liao, X., Lib, C., Wong, K.: Criteria for exponential stability of Cohen–Grossberg neural networks. Neural Netw. 17(10), 1407–1414 (2004)

    Article  Google Scholar 

  4. Cui, B., Wu, W.: Global exponential stability of Cohen–Grossberg neural networks with distributed delays. Neurocomputing 72(1–3), 386–391 (2008)

    Article  Google Scholar 

  5. Song, Q., Zhang, J.: Global exponential stability of impulsive Cohen–Grossberg neural network with time-varying delays. Nonlinear Anal.: Real. World Appl. 9(2), 500–510 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Li, T., Fei, S., Guo, Y., Zhu, Q.: Stability analysis on Cohen–Grossberg neural networks with both time-varying and continuously distributed delays. Nonlinear Anal., Real World Appl. 10(4), 2600–2612 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Zhang, J., Suda, Y., Komine, H.: Global exponential stability of Cohen–Grossberg neural networks with variable delays. Phys. Lett. A 338(1), 44–50 (2005)

    Article  MATH  Google Scholar 

  8. Wang, L., Zou, X.: Exponential stability of Cohen–Grossberg neural networks. Neural Netw. 15(3), 415–422 (2002)

    Article  Google Scholar 

  9. Zhao, J., Hill, D.J., Liu, T.: Synchronization of complex dynamical networks with switching topology: a switched system point of view. Automatica 45(11), 2502–2511 (2009)

    Article  MATH  Google Scholar 

  10. Lu, J., Ho, D.W.C., Wu, L.: Exponential stabilization of switched stochastic dynamical networks. Nonlinearity 22(4), 889–911 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Wang, D., Wang, W., Shi, P.: Robust fault detection for discrete-time switched linear systems with state delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39(3), 800–805 (2009)

    Article  Google Scholar 

  12. Fainshil, L., Margaliot, M., Chigansky, P.: On the stability of positive linear switched systems under arbitrary switching laws. IEEE Trans. Automat. Control 54(4), 2391–2396 (2009)

    MathSciNet  Google Scholar 

  13. Liu, X.: Stability analysis of switched positive systems: a switched linear copositive Lyapunov function method. IEEE Trans. Circuits Syst. II, Express Briefs 56(5), 414–418 (2009)

    Article  Google Scholar 

  14. Wu, L., Zheng, W.: Weighted H ∞ model reduction for linear switched systems with time-varying delay. Automatica 45(1), 186–193 (1999)

    Article  MathSciNet  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. Hespanha, J.P., Morse, A.S.: Stability of switched systems with average dwell time. In: Proceedings of the 38th IEEE Conference on Decision and Control, pp. 2655–2660 (1999)

  17. Zhai, G., Hu, B., Yasuda, K., Michel, A.N.: Disturbance attenuation properties of time-controlled switched systems. J. Franklin Inst. 338(7), 765–779 (1999)

    Article  MathSciNet  Google Scholar 

  18. Zhai, G., Hu, B., Yasuda, K., Michel, A.N.: Piecewise Lyapunov functions for switched systems with average dwell time. Asian J. Control 2(3), 192–197 (2000)

    Article  Google Scholar 

  19. Wang, D., Wang, W., Shi, P.: Exponential H ∞ filtering for switched linear systems with interval time-varying delay. Int. J. Robust Nonlinear Control 19(5), 532–551 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhang, L., Shi, P.: Stability, L 2-gain and asynchronous H ∞ control of discrete-time switched systems with average dwell time. IEEE Trans. Automat. Control 54(9), 2193–2200 (2009)

    MathSciNet  Google Scholar 

  21. Xie, D., Wang, Q., Wu, Y.: Average dwell-time approach to L 2 gain control synthesis of switched linear systems with time delay in detection of switching signal. IET Control Theory Appl. 3(6), 763–771 (2009)

    Article  MathSciNet  Google Scholar 

  22. Sun, X., Zhao, J., Hill, D.J.: Stability and L 2-gain analysis for switched delay system: a delay-dependent method. Automatica 42(10), 1769–1774 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  23. Zhang, W., Yu, L.: Stability analysis for discrete-time switched time-delay systems. Automatica 45(10), 2265–2271 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yuan, K., Cao, J., Li, H.: robust stability of switched Cohen–Grossberg neural networks with mixed time-varying delays. IEEE Trans. Syst. Man Cybern. 36(6), 1356–1363 (2006)

    Article  Google Scholar 

  25. Huang, H., Qu, Y., Li, H.: Robust stability analysis of switched hopfield neural networks with time-varying delay under uncertainty. Phys. Lett. A 345(4–6), 345–354 (2005)

    Article  MATH  Google Scholar 

  26. Li, P., Cao, J.: Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure. Nonlinear Dyn. 49(1–2), 295–305 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  27. Lou, X., Cui, B.: Delay-dependent criteria for global robust periodicity of uncertain switched recurrent neural networks with time-varying delay. IEEE Trans. Neural Netw. 19(4), 549–557 (2008)

    Article  Google Scholar 

  28. Liberzon, D., Hespanha, J.P., Morse, A.S.: Stability of switched systems: a Lie-algebraic condition. Syst. Control Lett. 37(3), 117–122 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  29. Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Decision and Control, pp. 2805–2810 (2000)

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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, P.R. China

    Jie Lian & Kai Zhang

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  1. Jie Lian
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  2. Kai Zhang
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Correspondence to Jie Lian.

Additional information

This work was supported by the NSF of China under Grant 61004040.

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Lian, J., Zhang, K. Exponential stability for switched Cohen–Grossberg neural networks with average dwell time. Nonlinear Dyn 63, 331–343 (2011). https://doi.org/10.1007/s11071-010-9807-2

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  • DOI: https://doi.org/10.1007/s11071-010-9807-2

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