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Further results on state estimation for neural networks of neutral-type with time-varying delay. (English) Zbl 1169.34334
The goal of the work is to estimate the neuron states of a neutral type network with time-varying delays through available output measurements for the first time. The authors consider the same problem for the same class of systems as in their previous work [Appl. Math. Comput. 203, No. 1, 217–223 (2008; Zbl 1166.34331)]. Based on Lyapunov methods and the linear matrix inequality, a novel criterion for the existence of the proposed state estimator of the network is given. This criterion differs from that one derived in [loc. cit.], however, it is proved by the technique analogous to that in the mentioned work.
##### MSC:
 34K35 Functional-differential equations connected with control problems 34K40 Neutral functional-differential equations 92B20 General theory of neural networks (mathematical biology)
##### Software:
LMI toolbox; LMI Control Toolbox
##### References:
 [1] Chua, L.; Yang, L.: Cellular neural networks: theory and applications, IEEE transactions on circuits and systems I 35, 257-1290 (1988) [2] Arik, S.; Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks, IEEE transactions on circuits and systems part I: Fundamental theory and applications 47, 571-574 (2000) · Zbl 0997.90095 · doi:10.1109/81.841859 [3] Park, J. H.: Global exponential stability of cellular neural networks with variable delays, Applied mathematics and computation 183, No. 2, 1214-1219 (2006) · Zbl 1115.34071 · doi:10.1016/j.amc.2006.06.046 [4] Cho, H. J.; Park, J. H.: Novel delay-dependent robust stability criterion of delayed cellular neural networks, Chaos, solitons, and fractals 32, No. 3, 1194-1200 (2007) · Zbl 1127.93352 · doi:10.1016/j.chaos.2005.11.040 [5] Park, J. H.: An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays, Chaos, solitons and fractals 32, No. 2, 800-807 (2007) · Zbl 1144.93023 · doi:10.1016/j.chaos.2005.11.106 [6] Rakkiyappan, R.; Balasubramaniam, P.: Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays, Applied mathematics and computation 198, 526-533 (2008) · Zbl 1144.34375 · doi:10.1016/j.amc.2007.08.053 [7] Kwon, O. M.; Park, J. H.: Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays, Applied mathematics and computation 203, No. 2, 813-823 (2008) · Zbl 1170.34052 · doi:10.1016/j.amc.2008.05.091 [8] J.H. Park, O.M. Kwon, Delay-dependent stability criterion for bidirectional associative memory neural networks with interval time-varying delays, Modern Physics Letters B, in press. · Zbl 1214.37059 · doi:10.1142/S0217984909017807 [9] Xu, S.; Shi, P.; Chu, Y.; Zou, Y.: Robust stochastic stabilization and H$\infty$ control of uncertain neutral stochastic time-delay systems, Journal of mathematical analysis and applications 314, 1-16 (2006) · Zbl 1127.93053 · doi:10.1016/j.jmaa.2005.03.088 [10] Kwon, O. M.; Park, J. H.: New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays, Applied mathematics and computation 205, No. 1, 417-427 (2008) · Zbl 1162.34060 · doi:10.1016/j.amc.2008.08.020 [11] Park, J. H.: A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos, solitons, and fractals 29, No. 2, 446-453 (2006) · Zbl 1121.92006 · doi:10.1016/j.chaos.2005.08.018 [12] Kwon, O. M.; Park, J. H.; Lee, S. M.: On global exponential stability for cellular neural networks with time-varying delays, Journal of applied mathematics and informatics 26, 961-972 (2008) [13] Arik, S.: An analysis of global asymptotic stability of delayed cellular neural networks, IEEE transactions of neural network 13, 1239-1242 (2002) [14] Park, J. H.: Robust stability of bidirectional associative memory neural networks with time delays, Physics letters A 349, No. 6, 494-499 (2006) [15] Xu, S.; Lam, J.; Ho, D. W. C.; Zou, Y.: Delay-dependent exponential stability for a class of neural networks with time delays, Journal of computational and applied mathematics 183, 16-28 (2005) · Zbl 1097.34057 · doi:10.1016/j.cam.2004.12.025 [16] Park, J. H.; Kwon, O. M.; Lee, S. M.: LMI optimization approach on stability for delayed neural networks of neutral-type, Applied mathematics and computation 196, No. 1, 236-244 (2008) · Zbl 1157.34056 · doi:10.1016/j.amc.2007.05.047 [17] Park, J. H.; Park, C. H.; Kwon, O. M.; Lee, S. M.: A new stability criterion for bidirectional associative memory neural networks of neutral-type, Applied mathematics and computation 199, 716-722 (2008) · Zbl 1149.34345 · doi:10.1016/j.amc.2007.10.032 [18] Wang, Z.; Ho, D. W. C.; Liu, X.: State estimation for delayed neural networks, IEEE transactions of neural networks 16, 279-284 (2005) [19] Huang, H.; Feng, G.; Cao, J.: An LMI approach to delay-dependent state estimation for delayed neural networks, Neurocomputing 71, 2857-2867 (2008) [20] Park, J. H.; Kwon, O. M.: Design of state estimator for neural networks of neutral-type, Applied mathematics and computation 202, No. 1, 360-369 (2008) · Zbl 1142.93016 · doi:10.1016/j.amc.2008.02.024 [21] Park, J. H.; Kwon, O. M.; Lee, S. M.: State estimation for neural networks of neutral-type with interval time-varying delay, Applied mathematics and computation 203, 217-223 (2008) · Zbl 1166.34331 · doi:10.1016/j.amc.2008.04.025 [22] K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proceedings of the 39th IEEE Conference of Decision and Control, 2000, pp. 2805 – 2810. [23] Zhu, X. L.; Yang, G. H.: Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay, IET control theory and applications 2, 524-534 (2008) [24] Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory, (1994) [25] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M.: LMI control toolbox user’s guide, (1995)