×

LMI-based criteria for robust stability of Cohen-Grossberg neural networks with delay. (English) Zbl 1137.93401

Summary: This Letter considers the robust stability analysis of delayed Cohen-Grossberg neural networks. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, several sufficient conditions guaranteeing the global robust convergence of the equilibrium point are derived. The main results are compared with some existing results and an error in an earlier publication is reported. An example is also given to illustrate the effectiveness of our results.

MSC:

93D09 Robust stability
37N35 Dynamical systems in control

Software:

LMI toolbox
Full Text: DOI

References:

[1] Liao, X.; Yu, J., IEEE Trans. Neural Networks, 9, 1042 (1998)
[2] Liao, X.; Wong, K.; Wu, Z.; Chen, G., IEEE Trans. Circuits Systems I, 48, 11, 1355 (2001) · Zbl 1006.34071
[3] Liao, X.; Wang, J.; Cao, J., Int. J. Neural Systems, 13, 3, 171 (2003)
[4] Singh, V., IEEE Proc. Control Theory Appl., 151, 1, 125 (2004)
[5] Arik, S., IEEE Trans. Circuits Systems I, 50, 1, 156 (2003) · Zbl 1368.93490
[6] Arik, S.; Tavsanoglu, V., IEEE Trans. Circuits Systems I, 47, 4, 571 (2000) · Zbl 0997.90095
[7] Arik, S., IEEE Trans. Circuits Systems I, 47, 1089 (2000) · Zbl 0992.93080
[8] Ye, H.; Michel, A.; Wang, K., IEEE Trans. Circuits Systems I, 43, 7, 532 (1996)
[9] Chen, T.; Rong, L., IEEE Trans. Neural Networks, 15, 1, 203 (2004)
[10] Lu, W.; Rong, L.; Chen, T., Int. J. Neural Systems, 13, 3, 193 (2003)
[11] Cohen, M.; Grossberg, S., IEEE Trans. Systems Man Cybernet., 13, 815 (1983) · Zbl 0553.92009
[12] Gopalsamy, K.; He, X., Physica D, 76, 344 (1994) · Zbl 0815.92001
[13] Joy, M., J. Math. Anal. Appl., 232, 61 (1999) · Zbl 0958.34057
[14] Liao, T.; Wang, F., IEEE Trans. Neural Networks, 11, 6, 1481 (2000)
[15] Cao, J., IEEE Trans. Circuits Systems I, 48, 11, 1330 (2001) · Zbl 1006.34070
[16] Li, Y., Chaos Solitons Fractals, 20, 459 (2004) · Zbl 1048.34118
[17] Arik, S., IEEE Trans. Neural Networks, 13, 5, 1239 (2002)
[18] Arik, S., IEEE Trans. Circuits Systems I, 49, 8, 1211 (2002) · Zbl 1368.34083
[19] Hwang, C.; Cheng, C.; Liao, T., Phys. Lett. A, 319, 157 (2003) · Zbl 1073.82597
[20] Liao, X.; Chen, G.; Sanchez, E., Neural Networks, 15, 855 (2002)
[21] Liao, X.; Chen, G.; Sanchez, E., IEEE Trans. Circuits Systems I, 49, 7, 1033 (2002)
[22] Van Den Driessche, P.; Zou, X., SIAM J. Appl. Math., 58, 6, 1878 (1998) · Zbl 0917.34036
[23] Chen, T.; Rong, L., Phys. Lett. A, 317, 436 (2003) · Zbl 1030.92002
[24] Wang, L.; Zou, X., Physica D, 170, 162 (2002) · Zbl 1025.92002
[25] Wang, L.; Zou, X., Neural Networks, 15, 415 (2002)
[26] Ye, H.; Michel, A.; Wang, K., Phys. Rev. E, 51, 2611 (1995)
[27] Xu, S.; Lam, J.; Ho, D.; Zou, Y., Phys. Lett. A, 325, 124 (2004) · Zbl 1161.93335
[28] Xie, L.; Fu, M.; de Souza, C., IEEE Trans. Automat. Control, 37, 8, 1253 (1992) · Zbl 0764.93067
[29] Du, C.; Xie, L., IEEE Trans. Circuits Systems I, 46, 11, 1371 (1999) · Zbl 0970.93037
[30] Yang, F.; Hung, Y., IEEE Trans. Circuits Systems I, 49, 8, 1236 (2002) · Zbl 1368.93733
[31] Rong, L.; Lu, W.; Chen, T., Chin. Ann. Math., 25, 2, 255 (2004) · Zbl 1063.34073
[32] Boyd, S., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004
[33] Shampine, L.; Thompson, S., Appl. Numer. Math., 37, 441 (2001) · Zbl 0983.65079
[34] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M., LMI Control Toolbox—For Use with Matlab (1995), MATH Works
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.