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A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays. (English) Zbl 1225.93096
Summary: The problem of exponential passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing new augmented Lyapunov-Krasovskii’s functionals and some novel analysis techniques, improved delay-dependent criteria for checking the exponential 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. A numerical example is included to show the superiority of our results.
MSC:
93D25Input-output approaches to stability of control systems
92B20General theory of neural networks (mathematical biology)
34H05ODE in connection with control problems
References:
[1]Ramesh, M.; Narayanan, S.: Chaos control of bonhoeffer – van der Pol oscillator using neural networks, Chaos, solitons and fractals 12, 2395-2405 (2001) · Zbl 1004.37067 · doi:10.1016/S0960-0779(00)00200-9
[2]Cannas, B.; Cincotti, S.; Marchesi, M.; Pilo, F.: Leaning of Chua’s circuit attractors by locally recurrent neural networks, Chaos, solitons and fractals 12, 2109-2115 (2001) · Zbl 0981.68135 · doi:10.1016/S0960-0779(00)00174-0
[3]Otawara, K.; Fan, L. T.; Tsutsumi, A.; Yano, T.; Kuramoto, K.; Yoshida, K.: An artificial neural network as a model for chaotic behavior of a three-phase fluidized bed, Chaos, solitons and fractals 13, 353-362 (2002) · Zbl 1073.76656 · doi:10.1016/S0960-0779(00)00250-2
[4]Ensari, T.; Arik, S.: Global stability of a class of neural networks with time-varying delay, IEEE transactions circuits systems II 52, 126-130 (2005)
[5]Xu, S.; Lam, J.; Ho, D. W. C.: Novel global robust stability criteria for interval neural networks with multiple time-varying delays, Physical letters A 342, 322-330 (2005) · Zbl 1222.93178 · doi:10.1016/j.physleta.2005.05.016
[6]Cao, J.; Yuan, K.; Li, H. X.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays, IEEE transactions neural networks 17, 1646-1651 (2006)
[7]Li, T.; Guo, L.; Sun, C.; Lin, C.: Further results on delay-dependent stability criteria of neural networks with time-varying delays, IEEE transactions neural networks 19, 726-730 (2008)
[8]Kwon, O. M.; Park, J. H.; Lee, S. M.: On robust stability for uncertain cellular neural networks with interval time-varying delays, IET control of theory and applications 2, 625-634 (2008)
[9]Kwon, O. M.; Park, J. H.: Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays, Applied mathematics of computing A 203, 813-823 (2008) · Zbl 1170.34052 · doi:10.1016/j.amc.2008.05.091
[10]Kwon, O. M.; Park, J. H.: New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays, Applications mathematics of computing A 205, 417-427 (2008) · Zbl 1162.34060 · doi:10.1016/j.amc.2008.08.020
[11]Park, J. H.: Further results on passivity analysis of delayed cellular neural networks, Chaos, solitons and fractals 34, 1546-1551 (2007) · Zbl 1152.34380 · doi:10.1016/j.chaos.2005.04.124
[12]Willems, J. C.: Dissipative dynamical systems, Archive of rational mechanics analysis 45, 321-393 (2008)
[13]Xu, S.; Zheng, W. X.; Zou, Y.: Passivity analysis of neural networks with time-varying delays, IEEE transactions circuits systems II 56, 325-329 (2009)
[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 letters 30, 155-169 (2009)
[15]Chellaboina, V.; Haddad, W. M.: Exponentially dissipative nonlinear dynamical systems: a nonlinear extension of strict positive realness, Journal of mathematics problems and engineering 1, 25-45 (2003) · Zbl 1075.93034 · doi:10.1155/S1024123X03202015
[16]Fradkov, A. L.; Hill, D. J.: Exponential feedback passivity and stabilizability of nonlinear systems, Automatica 34, 697-703 (1998) · Zbl 0937.93036 · doi:10.1016/S0005-1098(97)00230-6
[17]Hayakawa, T.; Haddad, W. M.; Bailey, J. M.; Hovakimyan, N.: Passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems, IEEE transactions neural network 16, 387-398 (2005)
[18]Zhu, S.; Shen, Y.; Chen, C.: Exponential passivity of neural networks with time-varying delay and uncertainty, Physical letters A 375, 136-142 (2010)
[19]K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of 39th IEEE Conference on Decision Control, December 2000, Sydney, Australia, pp. 2805 – 2810.
[20]Skelton, R. E.; Iwasaki, T.; Grigoradis, K. M.: A unified algebraic approach to linear control design, (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. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994)