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On improved passivity criteria of uncertain neural networks with time-varying delays. (English) Zbl 1243.93028
Summary: In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov-Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of Linear Matrix Inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.

MSC:
93B35 Sensitivity (robustness)
93C41 Control/observation systems with incomplete information
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Ensari, T., Arik, S.: Global stability of a class of neural networks with time-varying delay. IEEE Trans. Circuits Syst. II 52, 126–130 (2005) · Zbl 1365.93423 · doi:10.1109/TCSII.2004.842050
[2] Xu, S., Lam, J., Ho, D.W.C.: Novel global robust stability criteria for interval neural networks with multiple time-varying delays. Phys. Lett. A 342, 322–330 (2005) · Zbl 1222.93178 · doi:10.1016/j.physleta.2005.05.016
[3] Cao, J., Yuan, K., Li, H.-X.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17, 1646–1651 (2006) · doi:10.1109/TNN.2006.881488
[4] Li, T., Guo, L., Sun, C., Lin, C.: Further results on delay-dependent stability criteria of neural networks with time-varying delays. IEEE Trans. Neural Netw. 19, 726–730 (2008) · doi:10.1109/TNN.2007.914162
[5] Zhum, X.-L., Yang, G.-H.: New delay-dependent stability results for neural networks with time-varying delay. IEEE Trans. Neural Netw. 19, 1783–1791 (2008) · doi:10.1109/TNN.2008.2002436
[6] Kwon, O.M., Park, J.H., Lee, S.M.: On robust stability for uncertain cellular neural networks with interval time-varying delays. IET Control Theory Appl. 2, 625–634 (2008) · doi:10.1049/iet-cta:20070325
[7] Park, J.H.: Further results on passivity analysis of delayed cellular neural networks. Chaos Solitons Fractals 34, 1546–1551 (2007) · Zbl 1152.34380 · doi:10.1016/j.chaos.2005.04.124
[8] Willems, J.C.: Dissipative dynamical systems. Arch. Ration. Mech. Anal. 45, 321–393 (2008) · Zbl 0252.93002 · doi:10.1007/BF00276493
[9] Chen, B., Li, H., Lin, C., Zhou, Q.: Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays. Phys. Lett. A 373, 1242–1248 (2008) · Zbl 1228.92002 · doi:10.1016/j.physleta.2009.01.047
[10] Xu, S., Zheng, W.X., Zou, Y.: Passivity analysis of neural networks with time-varying delays. IEEE Trans. Circuits Syst. II 56, 325–329 (2009) · doi:10.1109/TCSII.2009.2015399
[11] Balasubramaniam, P., Nagamani, G.: Passivity analysis of neural networks with Markovian jumping parameters and interval time-varying delays. Nonlinear Anal. Hybrid Syst 4, 853–864 (2010) · Zbl 1208.93124 · doi:10.1016/j.nahs.2010.07.002
[12] Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Global passivity analysis of interval neural networks with discrete and distributed delays of neutral type. Neural Process. Lett. 32, 109–130 (2010) · Zbl 05802936 · doi:10.1007/s11063-010-9147-8
[13] Fu, J., Zhang, H., Ma, T., Zhang, Q.: On passivity analysis for stochastic neural networks with interval time-varying delay. Neurocomputing 73, 795–801 (2010) · Zbl 05721275 · doi:10.1016/j.neucom.2009.10.010
[14] Chen, Y., Li, W., Bi, W.: Improved results on passivity analysis of uncertain neural networks with time-varying discrete and distributed delays. Neural Process. Lett. 30, 155–169 (2009) · Zbl 05802905 · doi:10.1007/s11063-009-9116-2
[15] Zhang, Y., Yue, D., Tian, E.: New stability criteria of neural networks with interval time-varying delay: A piecewise delay method. Appl. Math. Comput. 208, 249–259 (2009) · Zbl 1171.34048 · doi:10.1016/j.amc.2008.11.046
[16] Ariba, Y., Gouaisbaut, F.: Delay-dependent stability analysis of linear systems with time-varying delay. In: Proceedings of 46th IEEE Conference on Decision Control, December, New Orleans, LA, pp. 2053–2058 (2007)
[17] Sun, J., Liu, G.P., Chen, J.: Delay-dependent stability and stabilization of neutral time-delay systems. Int. J. Robust Nonlinear Control 19, 1364–1375 (2009) · Zbl 1169.93399 · doi:10.1002/rnc.1384
[18] Sun, J., Liu, G.P., Chen, J., Rees, D.: Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46, 466–470 (2010) · Zbl 1205.93139 · doi:10.1016/j.automatica.2009.11.002
[19] Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE Conference on Decision Control, December, Sydney, Australia, pp. 2805–2810 (2000)
[20] Skelton, R.E., Iwasaki, T., Grigoradis, K.M.: A Unified Algebraic Approach to Linear Control Design. Taylor and Francis, New York (1997)
[21] Shao, H.: New delay-dependent stability criteria for systems with interval delay. Automatica 45, 744–749 (2009) · Zbl 1168.93387 · doi:10.1016/j.automatica.2008.09.010
[22] Boyd, S., Ghaoui, L.El., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) · Zbl 0816.93004
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