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Linear Matrix Inequality Optimization Approach to Exponential Robust Filtering for Switched Hopfield Neural Networks

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Abstract

This paper is concerned with the delay-dependent exponential robust filtering problem for switched Hopfield neural networks with time-delay. A new delay-dependent switched exponential robust filter is proposed that results in an exponentially stable filtering error system with a guaranteed robust performance. The design of the switched exponential robust filter for these types of neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated using standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed filter.

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References

  1. Hopfield, J.J.: Neurons with grade response have collective computational properties like those of a two-state neurons. Proc. Natl. Acad. Sci. 81, 3088–3092 (1984)

    Article  Google Scholar 

  2. Gupta, M.M., Jin, L., Homma, N.: Static and Dynamic Neural Networks. Wiley-Interscience, New York (2003)

    Book  Google Scholar 

  3. 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  MATH  Google Scholar 

  4. Lou, X.Y., Cui, B.T.: Delay-dependent criteria for robust stability of uncertain switched Hopfield neural networks. Int. J. Autom. Comput. 4, 304–314 (2007)

    Article  Google Scholar 

  5. Ahn, C.K.: An \(\mathcal{H}_{\infty}\) approach to stability analysis of switched Hopfield neural networks with time-delay. Nonlinear Dyn. 60, 703–711 (2010)

    Article  MATH  Google Scholar 

  6. Wang, Z., Ho, D.W.C., Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16, 279–284 (2005)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  8. Liu, Y., Wang, Z., Liu, X.: Design of exponential state estimators for neural networks with mixed time delays. Phys. Lett. A 364, 401–412 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Stoorvogel, A.: The \(\mathcal{H}_{\infty}\) Control Problem: A State-Space Approach. Prentice Hall, London (1992)

    MATH  Google Scholar 

  11. Huang, H., Feng, G.: Delay-dependent \(\mathcal{H}_{\infty}\) and generalized \(\mathcal{H}_{2}\) filtering for delayed neural networks. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 56, 846–857 (2009)

    Article  MathSciNet  Google Scholar 

  12. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishinan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)

    Book  Google Scholar 

  13. Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The MathWorks, Inc., Natik (1995)

    Google Scholar 

  14. Narendra, K.S., Tripathi, S.S.: Identification and optimization of aircraft dynamics. J. Aircr. 10, 193–199 (1973)

    Article  Google Scholar 

  15. Noldus, E.: Stabilization of a class of distributional convolutional equations. Int. J. Control 41, 947–960 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. He, Y., Wu, M., She, J.H., Liu, G.P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Control Lett. 51, 57–65 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wu, M., He, Y., She, J.H., Liu, G.P.: Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 40, 1435–1439 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Choon Ki Ahn.

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Communicated by Emilio Frazzoli.

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Ahn, C.K. Linear Matrix Inequality Optimization Approach to Exponential Robust Filtering for Switched Hopfield Neural Networks. J Optim Theory Appl 154, 573–587 (2012). https://doi.org/10.1007/s10957-012-0008-7

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  • DOI: https://doi.org/10.1007/s10957-012-0008-7

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