Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach

Nonlinear Dynamics

Volumn 73, Issue 3, 2013, Pages 1367-1383

  Rakkiyappan, R ^a   Zhu, Quanxin ^b   Radhika, T ^a  

^a BHARATHIAR UNIVERSITY   (India)

^b NANJING NORMAL UNIVERSITY   (China)

Author keywords

leakage time varying delay; Lyapunov Krasovskii functional; neural network; Sampled data; state estimator

Indexed keywords

CONTINUOUS MEASUREMENTS; DELAY DEPENDENT STABILITY CRITERION; INTEGRAL INEQUALITIES; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN JUMPING PARAMETERS; SAMPLED DATA; STATE ESTIMATORS; TIME-VARYING DELAY;

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; STABILITY CRITERIA; STATE ESTIMATION; TIME VARYING CONTROL SYSTEMS;

MARKOV PROCESSES;

EID: 84880919463     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0870-3     Document Type: Article

References (49)

1. Hagan, M.T., Demuth, H.B., Beale, M.: Neural Network Design. PWS Publishing Company, Boston (1996)
2. Gupta, M.M., Jin, L., Homma, N.: Static and Dynamic Neural Networks: from Fundamentals to Advanced Theory. Wiley, New York (2003)
3. Cichoki, A., Unbehauen, R.: Neural Networks for Optimization and Signal Processing. Wiley, Chichester (1993)
4. Haykin, S.: Neural Networks: a Comprehensive Foundation. Prentice Hall, New York (1998)
5. Ahn, C.K.: Robust stability of recurrent neural networks with ISS learning algorithm. Nonlinear Dyn. 65, 413-419 (2011)
6. Haken, H.: Pattern recognition and synchronization in pulse-coupled neural networks. Nonlinear Dyn. 44, 269-276 (2006)
7. Hendzel, Z.: An adaptive critic neural network for motion control of a wheeled mobile robot. Nonlinear Dyn. 50, 849-855 (2007)
8. Civalleri, P.P., Gilli, M., Pandolfi, L.: On stability of cellular neural networks with delay. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 40, 157-165 (1993)
9. Marcus, C.M., Westervelt, R.M.: Stability of analog neural networks with delay. Phys. Rev. A 39, 347-359 (1989)
10. Cao, J.: Global stability conditions for delayed CNNs. IEEE Trans. Circuits Syst. I 48, 1330-1333 (2001)
11. Liao, T.L., Wang, F.C.: Global stability for cellular neural networks with time delay. IEEE Trans. Neural Netw. 11, 1481-1484 (2000)
12. Li, X., Cao, J.: Delay-dependent stability of neural networks of neutral-type with time delay in the leakage term. Nonlinearity 23, 1709-1726 (2010)
13. Fu, X., Li, X., Akca, H.: Exponential state estimation for impulsive neural networks with time delay in the leakage term. Arab. J. Math. (2012). doi: 10.1007/s40065-012-0045-y
14. Zhu, Q., Cao, J.: Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 21, 1314-1325 (2010)
15. Zhu, Q., Cao, J.: Stability analysis of Markovian jump stochastic BAM neural networks with impulsive control and mixed time delays. IEEE Trans. Neural Netw. Learn. Syst. 23, 467-479 (2012)
16. Van Den Driessche, P., Zou, X.: Global attractivity in delayed Hopfield neural network models. SIAM J. Appl. Math. 6, 1878-1890 (1998)
17. Park, J., Kwon, O.: Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202, 360-369 (2008)
18. Park, J., Kwon, O.: Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl. Math. Comput. 208, 69-75 (2009)
19. Liu, Y., Wang, Z., Liu, X.: State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays. Phys. Lett. A 372, 7147-7155 (2008)
20. Balasubramaniam, P., Lakshmanan, S., Jeeva, S.: Sathya theesar, state estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60, 661-675 (2010)
21. Liu, Y., Wang, Z., Liang, J., Liu, X.: Synchronization and state estimation for discrete-time complex networks with distributed delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38, 1314-1325 (2008)
22. Shen, B., Wang, Z., Liu, X.: Bounded synchronization and state estimation for discrete time-varying stochastic complex networks over a finite horizon. IEEE Trans. Neural Netw. 22, 145-157 (2011)
23. Huang, H., Feng, G., Cao, J.: Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans. Neural Netw. 19, 1329-1339 (2008)
24. Liu, X., Cao, J.: Robust state estimation for neural networks with discontinuous activations. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40, 1425-1437 (2010)
25. Bao, H., Cao, J.: Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay. Neural Netw. 24, 19-28 (2011)
26. Huang, H., Feng, G., Cao, J.: Guaranteed performance state estimation of static neural networks with time-varying delay. Neurocomputing 74, 606-616 (2011)
27. 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. Nonlinear Dyn. 70, 1421-1434 (2012)
28. ∞ control. Syst. Control Lett. 54, 271-282 (2005)
29. Li, N., Hu, J., Hu, J., Li, L.: Exponential state estimation for delayed recurrent neural networks with sampled-data. Nonlinear Dyn. 69, 555-564 (2012)
30. Mikheev, Y., Sobolev, V., Fridman, E.: Asymptotic analysis of digital control systems. Autom. Remote Control 49, 1175-1180 (1988)
31. Astrom, K., Wittenmark, B.: Adaptive Control. Addison-Wesley, Reading (1989)
32. Fridman, E., Seuret, A., Richard, J.P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40, 1441-1446 (2004)
33. Wang, Z., Ho, D.W.C., Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16, 279-284 (2005)
34. Naghshtabrizi, P., Hespanha, J., Teel, A.: Exponential stability of impulsive systems with application to uncertain sampled-data systems. Syst. Control Lett. 57, 378-385 (2008)
35. Zhu, X.: Stabilization for sampled-data neural network based control systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 41, 210-221 (2011)
36. Naghshtabrizi, P., Hespanha, J., Teel, A.: Stability of delay impulsive systems with application to networked control systems. In: Proceedings of the 26th American Control Conference, New York, USA, July 2007
37. Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46, 421-427 (2010)
38. Liu, K., Fridman, E.: Stability analysis of networked sontrol systems: a discontinuous Lyapunov functional approach. In: Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, December 2009
39. Hardy, G., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1934)
40. Mirkin, L.: Some remarks on the use of time-varying delay to model sample and hold circuits. IEEE Trans. Autom. Control 52, 1109-1112 (2007)
41. Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46, 421-427 (2010)
42. Kharitonov, V., Niculescu, S.I., Moreno, J., Michiels, M.: Static output feedback stabilization: necessary conditions for multiple delay controllers. IEEE Trans. Autom. Control 52, 1109-1112 (2007)
43. Krasovskii, N.N., Lidskii, E.A.: Analysis and design of controllers in systems with random attributes. Autom. Remote Control 22, 1021-1025 (1961)
44. Kim, S., Li, H., Dougherty, E.R., Chao, N., Chen, Y., Bittner, M.L., Suh, E.B.: Can Markov chain models mimic biological regulation? J. Biol. Syst. 10, 337-357 (2002)
45. Wang, Z., Liu, Y., Liu, X.: State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw. 22, 41-48 (2009)
46. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht (1992)
47. Li, X., Fu, X.: Effects of leakage time-varying delay on stability of nonlinear differential systems. Journal of Franklin Institute. doi: 10.2016/j.jfranklin.2012.04.007
48. Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The Mathworks, Natick (1995)
49. Liu, Z., Yu, J., Xu, D., Peng, D.: Triple-integral method for the stability analysis of delayed neural networks. Neurocomputing 99, 283-289 (2013)