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Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay. (English) Zbl 1222.93213
Summary: This paper is concerned with the state estimation problem for a class of discrete-time stochastic neural networks (DSNNs) with random delays. The effect of both variation range and distribution probability of the time delay are taken into account in the proposed approach. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By employing a Lyapunov-Krasovskii functional, sufficient delay-distribution-dependent conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimator which can be checked readily by the Matlab toolbox. The main feature of the results obtained in this paper is that they are dependent on not only the bound but also the distribution probability of the time delay, and we obtain a larger allowance variation range of the delay, hence our results are less conservative than the traditional delay-independent ones. One example is given to illustrate the effectiveness of the proposed result.

##### MSC:
 9.3e+11 Estimation and detection in stochastic control theory
Matlab
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##### References:
 [1] Blythe, S.; Mao, X.; Liao, X., Stability of stochastic delay neural networks, Journal of the franklin institute, 338, 481-495, (2001) · Zbl 0991.93120 [2] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004 [3] Elanayar, V.T.S.; Shin, Y.C., Approximation and estimation of nonlinear stochastic dynamic systems using radial basis function neural networks, IEEE transactions on neural networks, 5, 594-603, (1994) [4] Fantacci, R.; Forti, M.; Marini, M.; Pancani, L., Cellular neural network approach to a class of communication problems, IEEE transactions on circuits and systems I, 46, 1457-1467, (1999) [5] Gao, H.; Lam, J.; Wang, C.; Wang, Y., Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay, IEE proceeding control theory and applications, 151, 691-698, (2004) [6] Habtom, R.; Litz, L., Estimation of unmeasured inputs using recurrent neural networks and the extended Kalman filter, Proceedings of the international conference on neural networks, 4, 2067-2071, (1997) [7] Haykin, S., Neural networks: a comprehensive foundation, (1998), Prentice Hall NJ · Zbl 0828.68103 [8] He, Y.; Wang, Q.G.; Wu, M.; Lin, C., State estimation for delayed neural networks, IEEE transactions on neural networks, 17, 1077-1081, (2006) [9] Hirasawa, K.; Mabu, S.; Hu, J., Propagations and control of stochastic signals through universal learning networks, Neural networks, 19, 487-499, (2006) · Zbl 1103.68692 [10] Hopfield, J., Neural networks and physics systems with emergent collective computational abilities, Proceedings of the national Academy of sciences, 79, 388-396, (1982) · Zbl 1369.92007 [11] Joya, G.; Atencia, M.A.; Sandoval, F., Hopfield neural network for optimization: study of the different dynamic, Neurocomputing, 43, 219-237, (2002) · Zbl 1016.68076 [12] Liang, J.; Wang, Z.; Liu, X., State estimation for coupled uncertain stochastic networks with missing measurement and time-varying delays: the discrete-time case, IEEE transactions on neural networks, 20, 781-793, (2009) [13] Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural networks, 19, 667-675, (2006) · Zbl 1102.68569 [14] Liu, Y.; Wang, Z.; Liu, X., Design of exponential state estimators for neural networks with mixed time delays, Physics letters A, 364, 401-412, (2007) [15] Liu, Y.; Wang, Z.; Liang, J.; Liu, X., Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE transactions on systems, man and cybernetics B (cybernetics), 38, 1314-1325, (2008) [16] Liu, Y.; Wang, Z.; Liu, X., State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays, Physics letters A, 372, 7147-7155, (2008) · Zbl 1227.92002 [17] Mou, S.; Gao, H.; Qiang, W.; Fei, Z., State estimation for discrete-time neural networks with time-varying delays, Neurocomputing, 72, 643-647, (2008) [18] Ray, A., Output feedback control under randomly varying distributed delays, Journal of guidance, control and dynamics, 17, 701-711, (1994) · Zbl 0925.93291 [19] Salam, F.M.; Zhang, J., Adaptive neural observer with forward co-state propagation, Proceedings of the international joint conference on neural networks, 1, 675-680, (2001) [20] Sanchez, E.; Perez, J., Input-to-state stability (ISS) analysis for dynamic neural networks, IEEE transactions on circuits and systems I, fundamental theory and applications, 46, 1395-1398, (1999) · Zbl 0956.68133 [21] Sun, Y.; Cao, J.; Wang, Z., Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing, 70, 2477-2485, (2007) [22] Tang, Y.; Fang, J.; Xia, M.; Yu, D., Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays, Neurocomputing, 72, 3830-3838, (2009) [23] Wang, Z.; Ho, D.W.C.; Liu, X., State estimation for delayed neural networks, IEEE transactions on neural networks, 16, 279-284, (2005) [24] Wang, Z.; Shu, H.; Liu, Y.; Ho, D.W.C.; Liu, X., Robust stability analysis of generalized neural networks with discrete and distributed time delays, Chaos, solitons and fractals, 30, 886-896, (2006) · Zbl 1142.93401 [25] Wang, Z.; Yang, F.; Ho, D.W.C.; Liu, X., Robust $$H_\infty$$ filtering for stochastic time-delay systems with missing measurements, IEEE transactions on signal processing, 54, 2579-2587, (2006) · Zbl 1373.94729 [26] Wang, Z.; Liu, Y.; Liu, X., H-infinity filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica, 44, 1268-1277, (2008) · Zbl 1283.93284 [27] Wang, Z.; Liu, Y.; Liu, X., State estimation for jumping recurrent neural networks with discrete and distributed delays, Neural networks, 22, 41-48, (2009) · Zbl 1335.93125 [28] Wang, Z.; Wei, G.; Feng, G., Reliable H-infinity control for discrete-time piecewise linear systems with infinite distributed delays, Automatica, 45, 2991-2994, (2009) · Zbl 1192.93030 [29] Wang, Z.; Liu, Y.; Wei, G.; Liu, X., A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances, Automatica, 46, 543-548, (2010) · Zbl 1194.93134 [30] Wang, Z.; Wang, Y.; Liu, Y., Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time-delays, IEEE transactions on neural networks, 21, 11-25, (2010) [31] Yue, D.; Zhang, Y.; Tian, E.; Peng, C., Delay-distribution-dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delays, IEEE transactions on neural networks, 19, 1299-1306, (2008) [32] Zhang, Y.; Yue, D.; Tian, E., Robust delay-distribution-dependent exponential stability criteria of discrete-time stochastic neural networks with time-varying delays, Neurocomputing, 72, 1265-1273, (2009)
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