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Further Improvement on Delay-range-dependent Stability Criteria for Delayed Recurrent Neural Networks with Interval Time-varying Delays

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  • Control Theory and Applications
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Abstract

This paper considers the problem of delay-range-dependent stability analysis for a class of delayed recurrent neural networks (DRNNs) with a time-varying delay in a range. Based on the Lyapunov-Krasovskii functional and derive the time derivative of this with integral inequality approach (IIA), new delay-dependent stability criteria for the system are established in terms of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. Information about the lower bound of the delay is fully used in the Lyapunov functional. Two examples are given to illustrate the effectiveness and the reduced conservatism of the proposed results.

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References

  1. H. Li, Y. Gao, L. Wu, and H. Lam, “Fault detection for T-S fuzzy time-delay systems: delta operator and input-output methods,” IEEE Transactions on Cybernetics, vol. 45, no. 2, pp. 229–241, 2015. [click]

    Article  Google Scholar 

  2. Z. Feng and W. Zheng, “Improved stability condition for Takagi-Sugeno fuzzy systems with time-varying delay,” IEEE Transactions on Cybernetics, vol. 47, no. 3, pp. 661–670, 2016. [click]

    Article  Google Scholar 

  3. H. Li, Y. Gao, P. Shi, and X, Zhao “Output-feedback control for T-S fuzzy delta operator systems with time-varying delays via an input-output approach,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 4, pp. 1100–1112, 2015. [click]

    Article  Google Scholar 

  4. J. Cao and J. Wang, “Global exponential stability and periodicity of recurrent neural networks with time delays,” IEEE Transactions on Circuits and Systems I-Regular Papers, vol. 52, pp. 920–931, 2005. [click]

    Article  MathSciNet  MATH  Google Scholar 

  5. C. C. Hua, C. N. Long, and X. P. Guan, “New results on stability analysis of neural networks with time varying delays,” Physics Letters A, vol. 352, pp. 335–340, 2006.

    Article  MATH  Google Scholar 

  6. N. Ozcan and S. Arik, “Global robust stability analysis of neural networks with multiple time delays,” IEEE Transactions on Circuits and Systems I-Regular Papers, vol. 35, pp. 166–176, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  7. Y. Q. Bai and J. Chen, “New stability criteria for recurrent neural networks with interval time-varying delay,” Neurocomputing, vol. 12, pp. 179–184, 2013. [click]

    Article  Google Scholar 

  8. A. Bouzerdoum and T. R. Pattison, “Neural network for quadratic optimization with bound constraints,” IEEE Transactions on Neural Networks, vol. 4, pp. 293–303, 1993.

    Article  Google Scholar 

  9. H. Cho and J. Park, “Novel delay-dependent robust stability criterion of delayed cellular neural networks,” Chaos Solitons Fractals, vol. 32, pp. 1194–1200, 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. Y. He, G. Liu, and D. Rees, “New delay-dependent stability criteria for neural networks with time-varying delay,” IEEE Transactions on Neural Networks, vol. 18, pp. 310–314, 2007. [click]

    Article  Google Scholar 

  11. C. Li and X. Liao, “Robust stability and robust periodicity of delayed recurrent neural networks with noise disturbance,” IEEE Transactions on Circuits and Systems IRegular Papers, vol. 53, pp. 2265–2273, 2006.

    Article  Google Scholar 

  12. C. Li and G. Feng, “Delay-interval-dependent stability of recurrent neural networks with time-varying delay,” Neurocomputing, vol. 7, pp. 1179–1183, 2009.

    Article  Google Scholar 

  13. J. Li, A. N. Michel, and W. Porod, “Analysis and synthesis of a class of neural networks: linear systems operating on a closed hypercube,” IEEE Transactions on Circuits and Systems, vol. 36, pp. 1406–1422, 1989.

    MathSciNet  MATH  Google Scholar 

  14. P. L. Liu, “Further results on robust delay-range-dependent stability criteria for uncertain neural networks with interval time-varying delay,” International Journal of Control, Automation, and Systems, vol. 13, pp. 1140–1149, 2015. [click]

    Article  Google Scholar 

  15. J. Liang and J. Cao, “A based-on LMI stability criterion for delayed recurrent neural networks,” Chaos Solitons Fractals, vol. 28, pp. 154–160, 2006. [click]

    Article  MathSciNet  MATH  Google Scholar 

  16. C. Y. Lu, H. H. Tsai, T. J. Su, J. S. H. Tsai, and C.W. Liao, “A delay-dependent approach to passivity analysis for uncertain neural networks with time-varying delay,” Neural Process Letters, vol. 27, pp. 237–246, 2008. [click]

    Article  Google Scholar 

  17. S. Mou, H. Gao, W. Qiang, and K. Chen, “New delaydependent exponential stability for neural networks with time delays,” IEEE Transactions on Systems Man and Cybernetics-Part B-Cybernetics, vol. 38, pp. 571–576, 2008. [click]

    Article  Google Scholar 

  18. H. Shao, “Delay-dependent stability for recurrent neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, pp. 1647–165, 2008.

    Article  Google Scholar 

  19. H. Shao, “Novel delay-dependent stability results for neural networks with time-varying delays,” Circuits Systems and Signal Processing, vol. 29, pp. 637–647, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Shao, “Delay-dependent approaches to globally exponential stability for recurrent neural networks,” IEEE Transactions on Circuits and Systems II-Express Briefs, vol. 55, pp. 591–595, 2008.

    Article  Google Scholar 

  21. J. Sun and J. Chen, “Stability analysis of static recurrent neural networks with interval time-varying delay,” Applied Mathematics and Computation, vol. 22, pp. 111–120, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  22. Z. G. Wu, J. Lam, H. Su, and J. Chu, “Stability and dissipativity analysis of static neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 23, pp. 199–210, 2012. [click]

    Article  Google Scholar 

  23. S. Xu, J. Lam, D.W. C. Ho, and Y. Zhou, “Improved global robust asymptotic stability criteria for delayed cellular neural networks,” IEEE Transactions on Systems Man and Cybernetics-Part B-Cybernetics, vol. 35, pp. 1317–1321, 2005. [click]

    Article  Google Scholar 

  24. S. Xu, J. Lam, D. W. C. Ho, and Y. Zhou, “Novel global asymptotic stability criteria for delayed cellular neural network,” IEEE Transactions on Circuits and Systems IIExpress Briefs, vol. 52, pp. 349–353, 2005.

    Article  Google Scholar 

  25. S. Xu, J. Lam, D. W. C. Ho, and Y. Zhou, “A new LMI condition for delayed dependent asymptotic stability of delayed Hopfied neural networks,” IEEE Transactions on Circuits and Systems II-Express Briefs, vol. 52, pp. 230–234, 2006.

    Google Scholar 

  26. Q. F. Yang, Q. H. Ren, and X. M. Xie, “New delay dependent stability criteria for recurrent neural networks with interval time-varying delay,” ISA Transactions, vol. 53, pp. 994–999, 2014.

    Article  Google Scholar 

  27. Z. B. Xu, H. Qiao, J. Peng, and B. Zhang, “A comparative study on two modeling approaches in neural networks,” Neural Networks, vol. 17, pp. 73–85, 2004. [click]

    Article  MATH  Google Scholar 

  28. Z. Zeng, J. Wang, and X. Liao, “Global exponential stability of a general class of recurrent neural networks with time-varying delays,” IEEE Transactions on Circuits and Systems I-Regular Papers, vol. 50, pp. 1353–1358, 2003. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. B. Zhang, S. Xu, and Y. Zou, “Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays,” Neurocomputing, vol. 72, pp. 321–330, 2008. [click]

    Article  Google Scholar 

  30. Z. Zuo, C. Yang, and Y. Wang, “A new method for stability analysis of recurrent neural networks with interval timevarying delay,” IEEE Transactions Neural Networks, vol. 21, pp. 339–344, 2010. [click]

    Article  Google Scholar 

  31. L. B. Almeida, Back Propagation in Perceptrons with Feedback, in Neural Computers, ed. by R. Eckmiller, C. Von der Malsburg, Springer, New York, 1998.

  32. S. L. Boyd, G. E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Automation Engineering Institute of Mechatronoptic System, Chienkuo Technology University, Changhua, 500, Taiwan, Republic of China

    Pin-Lin Liu

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  1. Pin-Lin Liu
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Correspondence to Pin-Lin Liu.

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Recommended by Associate Editor Soohee Han under the direction of Editor PooGyeon Park.

Pin-Lin Liu received his B.S., M.S. and Ph.D. degrees from the National Changhua University of Education, Taiwan, in 1986, 1990, and 2001, respectively. In 1990, he joined the Department of Automation Engineering Institute of Mechatronoptic System, Chienkuo Technology University, Taiwan, where he is currently an Associate Professor. His research interests include time delay systems, robust control, green energy and its application.

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Liu, PL. Further Improvement on Delay-range-dependent Stability Criteria for Delayed Recurrent Neural Networks with Interval Time-varying Delays. Int. J. Control Autom. Syst. 16, 1186–1193 (2018). https://doi.org/10.1007/s12555-016-0359-1

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  • DOI: https://doi.org/10.1007/s12555-016-0359-1

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