State estimation of memristor-based recurrent neural networks with time-varying delays based on passivity theory

Complexity

Volumn 19, Issue 4, 2014, Pages 32-43

  Rakkiyappan, R ^a   Chandrasekar, A ^a   Laksmanan, S ^b   Park, Ju H ^c  

^a BHARATHIAR UNIVERSITY   (India)

^b UNITED ARAB EMIRATES UNIVERSITY   (United Arab Emirates)

^c Yeungnam University   (South Korea)

Author keywords

Memristor; Passivity; Recurrent neural networks; State estimation; Time varying delay

Indexed keywords

EID: 84897614854     PISSN: 10762787     EISSN: 10990526     Source Type: Journal    
DOI: 10.1002/cplx.21482     Document Type: Article

References (40)

1. Arik, S. An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans Neural Netw 2002, 13, 1239-1242.
2. Haykin, S. Neural Networks: A Comprehensive Foundation; Prentice-Hall: NJ, 1998.
3. Najarian, K. On learning of sigmoid neural networks. Complexity 2001, 6, 39-45.
4. Ebner, M.; Shackleton, M.; Shipman, R. How neutral networks influence evolvability. Complexity 2002, 7, 19-33.
5. Johnson, J.; Pictom, P. How to train a neural network: An introduction to the new computational paradigm. Complexity 1996, 1, 13-28.
6. Chen, T.; Wang, L. Global μ-stability of delayed neural networks with unbounded time varying delays. IEEE Trans Neural Netw 2007, 18, 1836-1840.
7. Rakkiyappan, R.; Balasubramaniam, P. Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl Math Comput 2008, 198, 526-533.
8. Bondarenko, V.E. Information processing, memories, and synchronization in chaotic neural network with the time delay. Complexity 2005, 11, 39-52.
9. Park, P.; Ko, J.W.; Jeong, C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica 2011, 47, 235-238.
10. Li, T.; Wang, T.; Song, A.; Fei, S. Combined convex technique on delay-dependent stability for delayed neural networks. IEEE Trans Neural Netw Learn Syst 2013, 24, 1459-1466.
11. Li, T.; Yang, X.; Yang, P.; Fei, S. New delay-variation-dependent stability for neural networks with time-varying delay. Neurocomputing 2013, 101, 361-369.
12. Byrnes, I.; Isidori, A.; Willems, J.C. Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems. IEEE Trans Automat Contr 1991, 36, 1228-1240.
13. Hill, D.J.; Moylan, P.J. The stability of nonlinear dissipative systems. IEEE Trans Automat Contr 1976, 21, 707-711.
14. Wu, C.W. Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion and observer design. IEEE Trans Circuits Syst I 2001, 48, 1257-1261.
15. Wu, L.; Zheng, W.X. Passivity-based sliding mode control of uncertain singular time-delay systems. Automatica 2009, 45, 2120-2127.
16. Zhao, Z.; Song, Q.; He, S. Passivity analysis of stochastic neural networks with time-varying delays and leakage delay. Neurocomputing. http://dx.doi.org/10.1016/j.neucom.2012.08.049.
17. Balasubramaniam, P.; Nagamani, G.; Rakkiyappan, R. Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun Nonlin Sci Numer Simulat 2011, 16, 4422-4437.
18. Huang, H.; Feng, G. State estimation of recurrent neural networks with time varying delay: A novel delay partition approach. Neurocomputing 2011, 74, 792-796.
19. Huang, H.; Feng, G.; Cao, J. Guaranteed performance state estimation of static neural networks with time-varying delay. Neurocomputing 2011, 74, 606-616.
20. Wang, Z.; Ho, D.W.C.; Liu, X. State estimation for delayed neural networks. IEEE Trans Neural Netw 2005, 16, 279-284.
21. He, Y.; Wang, Q.; Wu, M.; Lin, C. Delay-dependent state estimation for delayed neural networks. IEEE Trans Neural Netw 2006, 17, 1077-1081.
22. Huang, H.; Feng, G.; Cao, J. An LMI approach to delay dependent state estimation for delayed neural networks. Neurocomputing 2008, 71, 2857-2867.
23. Chua, L.O. Memristor-the missing circuit element. IEEE Trans Circ Theory 1971, CT-18, 507-519.
24. Strukov, D.B.; Snider, G.S.; Stewart, G.R.; Williams, R.S. The missing memristor found. Nature 2008, 453, 80-83.
25. Wen, S.; Zeng, Z. Dynamics analysis of a class of memristor-based recurrent networks with time-varying delays in the presence of strong external stimuli. Neural Process Lett 2012, 35, 47-59.
26. Wu, A.; Zeng, Z. Passivity analysis of memristive neural networks with different memductance functions. Commun Nonlin Sci Numer Simul 2014, 19, 274-285.
27. Forti, M.; Nistri, P. Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst I 2003, 50, 1421-1435.
28. Clarke, F.; Ledyaev, Y.; Stem, R.; Wolenski, R. Nonsmooth Analysis and Control Theory; Springer: New York, 1988.
29. Filippov, A. Differential Equations with Discontinuous Right-Hand Side, Mathematics its Applications; Kluwer Academic: Boston, MA, 1988.
30. Bacciotti, A.; Rosier, L. Lyapunov Functions and Stability in Control Theory; Springer: Berlin, 2005.
31. Byrnes, C.; Isidori, A.; Willem, J. Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear system. IEEE Trans Autom Contr 1991, 36, 1228-1240.
32. Kwon, O.M.; Lee, S.M.; Park, J.H.; Cha, E.J. New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput 2012, 218, 9953-9964.
33. Tian, J.K.; Zhong, S.M. Improved delay-dependent stability criterion for neural networks with time-varying delay. Appl Math Comput 2011, 217, 10278-10288.
34. Yue, D.; Tian, E.G.; Zhang, Y.J.; Peng, C. Delay distribution dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay. IEEE Trans Syst Man Cybern B Cybern 2010, 39, 503-516.
35. Liu, J.; Zhang, J. Note on stability of discrete-time time-varying delay systems. IET Contr Theory Appl 2012, 6, 335-339.
36. Yue, D.; Tian, E.G.; Zhang, Y.J. A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay. Int J Robust Nonlin Contr 2008, 19, 1493-1518.
37. Yang, R.N.; Zhang, Z.X.; Shi, P. Exponential stability on stochastic neural networks with discrete interval and distributed delays. IEEE Trans Neural Netw 2010, 21, 169-175.
38. Wen, S.; Zeng, Z.; Huang, T.; Chen, Y. Passivity analysis of memristor-based recurrent neural networks with time-varying delays. J Franklin Inst 2013, 350, 2354-2370.
39. Ahn, C.K. Switched exponential state estimation of neural networks based on passivity theory. Nonlin Dyn 2012, 67, 573-586.
40. Lakshmanan, S.; Park, J.H.; Ji, D.H.; Jung, H.Y.; Nagamani, G. State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. Nonlin Dyn 2012, 70, 1421-1434.