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Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters

  • Zhang He
  • Junwei Lu
  • Yunliang Wei
  • Yuming Chu
Article
  • 74 Downloads

Abstract

This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples.

Keywords

Markov jump Reachable set estimation Bidirectional associative memory NNSs Piecewise-constant transition rates Time delay 

Mathematics Subject Classification

00-01 99-00 

Notes

Acknowledgements

This work was supported in part supported by both the National Natural Science Foundation of China under Grants 11401062 and 61374104, NSFC 61374086, the Natural Science Foundation of Jiangsu Province under Grant BK20140770, BK20131097. The authors would like to express sincere appreciation to the editor and anonymous reviewers for their valuable comments which have led to an improvement in the presentation of the paper.

References

  1. Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory, vol 15. Society for Industrial and Applied Mathematics (SIAM)Google Scholar
  2. Cao J, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172CrossRefMATHGoogle Scholar
  3. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circ Syst I Regul Pap 52(2):417–426MathSciNetCrossRefMATHGoogle Scholar
  4. Chen Y, Lam J, Zhang B (2016) Estimation and synthesis of reachable set for switched linear systems. Automatica 63:122–132MathSciNetCrossRefMATHGoogle Scholar
  5. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In Decision and Control, 2000. In: Proceedings of the 39th IEEE conference on, vol 3, pp 2805–2810). IEEE.  https://doi.org/10.1109/CDC.2000.914233
  6. He Y, Wu M, She JH (2006) An improved global asymptotic stability criterion for delayed cellular neural networks. IEEE Trans Neural Netw 17(1):250–252CrossRefGoogle Scholar
  7. He Y, Liu G, Rees D (2007) New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans Neural Netw 18(1):310–314CrossRefGoogle Scholar
  8. He X, Li C, Huang T, Li C, Huang J (2014) A recurrent neural network for solving bilevel linear programming problem. IEEE Trans Neural Netw Learn Syst 25(4):824–830CrossRefGoogle Scholar
  9. Huang T (2006) Exponential stability of fuzzy cellular neural networks with distributed delay. Phys Lett A 351(1):48–52CrossRefMATHGoogle Scholar
  10. Huang T, Li C, Duan S, Starzyk JA (2012) Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects. IEEE Trans Neural Netw Learn Syst 23(6):866–875CrossRefGoogle Scholar
  11. Huang H, Huang T, Chen X (2013) A mode-dependent approach to state estimation of recurrent neural networks with Markovian jumping parameters and mixed delays. Neural Netw 46:50–61CrossRefMATHGoogle Scholar
  12. Kwon OM, Lee SM, Park JH (2011) On the reachable set bounding of uncertain dynamic systems with time-varying delays and disturbances. Inf Sci 181(17):3735–3748MathSciNetCrossRefMATHGoogle Scholar
  13. Li C, Liao X (2005) Passivity analysis of neural networks with time delay. IEEE Trans Circ Syst II Express Briefs 52(8):471–475MathSciNetCrossRefGoogle Scholar
  14. Li H, Chen B, Zhou Q, Qian W (2009) Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans Syst Man Cybern Part B (Cybernetics) 39(1):94–102CrossRefGoogle Scholar
  15. Li C, Li C, Liao X, Huang T (2011) Impulsive effects on stability of high-order BAM neural networks with time delays. Neurocomputing 74(10):1541–1550CrossRefGoogle Scholar
  16. Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675CrossRefMATHGoogle Scholar
  17. Mou S, Gao H, Lam J, Qiang W (2008) A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. IEEE Trans Neural Netw 19(3):532–535CrossRefGoogle Scholar
  18. Nam PT, Pathirana PN (2011) Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays. Automatica 47(8):1838–1841MathSciNetCrossRefMATHGoogle Scholar
  19. Peng W, Wu Q, Zhang Z (2016) LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique. Neurocomputing 199:103–113CrossRefGoogle Scholar
  20. Qi J, Li C, Huang T (2015) Stability of inertial BAM neural network with time-varying delay via impulsive control. Neurocomputing 161:162–167CrossRefGoogle Scholar
  21. Vidyasagar M (1993) Nonlinear systems analysis, 2nd edn. Prentice-Hall, Englewood Cliffs, NJMATHGoogle Scholar
  22. Wu Z (2015) Stability criteria of random nonlinear systems and their applications. IEEE Trans Autom Control 60(4):1038–1049MathSciNetCrossRefMATHGoogle Scholar
  23. Zeng Z, Huang T, Zheng WX (2010) Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Trans Neural Netw 21(8):1371–1377CrossRefGoogle Scholar
  24. Zhang Z, Quan Z (2015) Global exponential stability via inequality technique for inertial BAM neural networks with time delays. Neurocomputing 151:1316–1326CrossRefGoogle Scholar
  25. Zhang H, Wang Y (2008) Stability analysis of Markovian jumping stochastic CohenCGrossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19(2):366–370CrossRefGoogle Scholar
  26. Zhang Z, Yu S (2016) Global asymptotic stability for a class of complex-valued CohenCGrossberg neural networks with time delays. Neurocomputing 171:1158–1166CrossRefGoogle Scholar
  27. Zhang W, Li C, Huang T, Tan J (2015) Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control. Neural Comput Appl 26(7):1781–1787CrossRefGoogle Scholar
  28. Zhang Z, Hao D, Zhou D (2017) Global asymptotic stability by complex-valued inequalities for complex-valued neural networks with delays on period time scales. Neurocomputing 219:494–501CrossRefGoogle Scholar
  29. Zuo Z, Ho DW, Wang Y (2010) Reachable set bounding for delayed systems with polytopic uncertainties: the maximal LyapunovCKrasovskii functional approach. Automatica 46(5):949–952MathSciNetCrossRefMATHGoogle Scholar
  30. Zuo Z, Ho DWC, Wang Y (2011) Reachable set estimation for linear systems in the presence of both discrete and distributed delays. IET Control Theory Appl 5(15):1808–1812MathSciNetCrossRefGoogle Scholar
  31. Zuo Z, Fu Y, Wang Y (2012) Results on reachable set estimation for linear systems with both discrete and distributed delays. IET Control Theory Appl 6(14):2346–2350MathSciNetCrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Science and TechnologyNanjingChina
  2. 2.School of Electrical and Automation EngineeringNanjing Normal UniversityNanjingChina
  3. 3.School of Mathematical SciencesQufu Normal UniversityQufuChina
  4. 4.School of ScienceHuzhou Teachers CollegeHuzhouChina

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