State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach. (English) Zbl 1281.92008
Summary: In this paper, the sampled-data state estimation problem is investigated for neural networks with time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled data estimator is constructed. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. New delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.
MSC:
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 93D30 | Lyapunov and storage functions |
| 93C57 | Sampled-data control/observation systems |
References:
| [1] | Chua, L., Yang, L.: Cellular neural networks: theory and applications. IEEE Trans. Circuits Syst. I 35, 1257-1290 (1988) · Zbl 0663.94022 · doi:10.1109/31.7600 |
| [2] | Cichoki, A., Unbehauen, R.: Neural Networks for Optimization and Signal Processing. Wiley, Chichester (1993) · Zbl 0824.68101 |
| [3] | Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall, New York (1998) · Zbl 0828.68103 |
| [4] | Roska, T., Chua, L.O.: Cellular neural networks with nonlinear and delay-type template. Int. J. Circuit Theory Appl. 20, 469-481 (1992) · Zbl 0775.92011 · doi:10.1002/cta.4490200504 |
| [5] | Xia, Y., Wang, J.: Global asymptotic and exponential stability of a dynamic neural system with asymmetric connection weights. IEEE Trans. Autom. Control 46, 635-658 (2001) · Zbl 1007.93062 · doi:10.1109/9.917666 |
| [6] | Gan, Q.: Adaptive synchronization of stochastic neural networks with mixed time delays and reaction diffusion terms. Nonlinear Dyn. 69, 2207-2219 (2012) · Zbl 1263.35143 · doi:10.1007/s11071-012-0420-4 |
| [7] | Hu, S., Wang, J.: Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks. IEEE Trans. Autom. Control 46, 802-807 (2002) · Zbl 1364.93680 |
| [8] | Tian, L., Liang, J., Cao, J.: Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays. Nonlinear Dyn. 67, 47-61 (2012) · Zbl 1242.93072 · doi:10.1007/s11071-011-9956-y |
| [9] | Liang, X., Wang, J.: An additive diagonal stability condition for absolute exponential stability of a general class of neural networks. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48, 1308-1317 (2001) · Zbl 1098.62557 · doi:10.1109/81.964419 |
| [10] | Wu, H., Tao, F., Qin, L., Shi, R., He, L.: Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions. Nonlinear Dyn. 66, 479-487 (2011) · Zbl 1242.93113 · doi:10.1007/s11071-010-9926-9 |
| [11] | Wang, Z., Ho, D.W.C., Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16, 279-284 (2005) · doi:10.1109/TNN.2004.841813 |
| [12] | Lou, X., Cui, B.: Design of state estimator for uncertain neural networks via the integral-inequality method. Nonlinear Dyn. 53, 223-235 (2008) · Zbl 1402.92023 · doi:10.1007/s11071-007-9310-6 |
| [13] | Huang, H., Feng, G.: A scaling parameter approach to delay-dependent state estimation of delayed neural networks. IEEE Trans. Circuits Syst. II, Express Briefs 57, 36-40 (2010) · doi:10.1109/TCSII.2009.2035271 |
| [14] | Huang, H., Feng, G.: State estimation of recurrent neural networks with time-varying delay: a novel delay partition approach. Neurocomputing 74, 792-796 (2011) · doi:10.1016/j.neucom.2010.10.006 |
| [15] | Park, J.H., Kwon, O.M.: Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202, 360-369 (2008) · Zbl 1142.93016 · doi:10.1016/j.amc.2008.02.024 |
| [16] | Park, J.H., Kwon, O.M., Lee, S.M.: State estimation for neural networks of neutral-type with interval time-varying delays. Appl. Math. Comput. 203, 217-223 (2008) · Zbl 1166.34331 · doi:10.1016/j.amc.2008.04.025 |
| [17] | Park, J.H., Kwon, O.M.: Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl. Math. Comput. 208, 69-75 (2009) · Zbl 1169.34334 · doi:10.1016/j.amc.2008.11.017 |
| [18] | Li, T., Fei, S.M., Zhu, Q.: Design of exponential state estimator for neural networks with distributed delays. Nonlinear Anal., Real World Appl. 10, 1229-1242 (2009) · Zbl 1167.93318 · doi:10.1016/j.nonrwa.2007.10.017 |
| [19] | Ahn, C.K.: Switched exponential state estimation of neural networks based on passivity theory. Nonlinear Dyn. 67, 573-586 (2012) · Zbl 1242.93036 · doi:10.1007/s11071-011-0010-x |
| [20] | Huang, H., Feng, G., Cao, J.: Guaranteed performance state estimation of static neural networks with time-varying delay. Neurocomputing 74, 606-616 (2011) · doi:10.1016/j.neucom.2010.09.017 |
| [21] | Balasubramaniam, P., Lakshmanan, S., Jeeva Sathya Theesar, S.: State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60, 661-675 (2009) · Zbl 1194.62109 · doi:10.1007/s11071-009-9623-8 |
| [22] | Chen, Y., Bi, W., Li, W., Wu, Y.: Less conservative results of state estimation for neural networks with time-varying delay. Neurocomputing 73, 1324-1331 (2010) · doi:10.1016/j.neucom.2009.12.019 |
| [23] | Wang, H., Song, Q.: State estimation for neural networks with mixed interval time-varying delays. Neurocomputing 73, 1281-1288 (2010) · doi:10.1016/j.neucom.2009.12.017 |
| [24] | 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) · Zbl 1268.92012 · doi:10.1007/s11071-012-0544-6 |
| [25] | Wang, Z., Liu, Y., Liu, X.: State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw. 22, 41-48 (2009) · Zbl 1335.93125 · doi:10.1016/j.neunet.2008.09.015 |
| [26] | Jin, L., Nikiforuk, P.N., Gupta, M.M.: Adaptive control of discrete-time nonlinear systems using recurrent neural networks. IEE Proc., Control Theory Appl. 141, 169-176 (1994) · Zbl 0803.93026 · doi:10.1049/ip-cta:19949976 |
| [27] | Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control Syst. Mag. 21, 84-99 (2001) · doi:10.1109/37.898794 |
| [28] | Lam, H.K., Leung, F.H.F.: Design and stabilization of sampled-data neural-network-based control systems. IEEE Trans. Syst. Man Cybern., B Cybern. 36, 995-1005 (2006) · doi:10.1109/TSMCB.2006.872262 |
| [29] | 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) · Zbl 1140.93036 · doi:10.1016/j.sysconle.2007.10.009 |
| [30] | Zhu, X.-L., Wang, Y.: Stabilization for sampled-data neural-network-based control systems. IEEE Trans. Syst. Man Cybern., B Cybern. 41, 210-221 (2011) · Zbl 1260.47004 · doi:10.1109/TSMCB.2010.2050587 |
| [31] | Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46, 421-427 (2010) · Zbl 1205.93099 · doi:10.1016/j.automatica.2009.11.017 |
| [32] | Lam, H.K., Leung, F.H.F.: Sampled-data fuzzy controller for time-delay nonlinear systems: fuzzy-model-based LMI approach. IEEE Trans. Syst. Man Cybern., B Cybern. 37, 617-629 (2007) · doi:10.1109/TSMCB.2006.889629 |
| [33] | Gan, Q., Liang, Y.: Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J. Franklin Inst. 349, 1955-1971 (2012) · Zbl 1300.93113 · doi:10.1016/j.jfranklin.2012.05.001 |
| [34] | Zhang, C.K., He, Y., Wu, M.: Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing 74, 265-273 (2010) · doi:10.1016/j.neucom.2010.03.020 |
| [35] | Liu, K., Fridman, E.: Wirtinger’s inequality and Lyapunov-based sampled-data stabilization. Automatica 48, 102-108 (2012) · Zbl 1244.93094 · doi:10.1016/j.automatica.2011.09.029 |
| [36] | Wu, Z.-G., Park, J.H., Su, H., Chu, J.: Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data. Nonlinear Dyn. 69, 2021-2030 (2012) · Zbl 1263.34075 · doi:10.1007/s11071-012-0404-4 |
| [37] | 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) · Zbl 1253.93082 · doi:10.1007/s11071-011-0286-x |
| [38] | Liu, K., Suplin, V., Fridman, E.: Stability of linear systems with general sawtooth delay. IMA J. Math. Control Inf. 27, 419-436 (2011) · Zbl 1206.93080 · doi:10.1093/imamci/dnq023 |
| [39] | Gu, K., Kharitonov, V.K., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Boston (2003) · Zbl 1039.34067 · doi:10.1007/978-1-4612-0039-0 |
| [40] | Zhang, X.M., Han, Q.-L.: Novel delay-derivative-dependent stability criteria using new bounding techniques. Int. J. Robust Nonlinear Control. doi:10.1002/rnc.2829 (2012) · Zbl 1278.93230 · doi:10.1002/rnc.2829 |
| [41] | Zhang, D., Yu, L.: \( \mathcal{H}_{\infty}\) filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations. J. Franklin Inst. 347, 1374-1390 (2010) · Zbl 1202.93047 · doi:10.1016/j.jfranklin.2010.05.001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
