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Global exponential stability results for neutral-type impulsive neural networks. (English) Zbl 1186.34101

Summary: By using a Lyapunov-Krasovkii functional and combining it with the linear matrix inequality (LMI) approach, we analyze the global exponential stability of neutral-type impulsive neural networks. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.

MSC:

34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K45 Functional-differential equations with impulses

Software:

LMI toolbox; Matlab
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Full Text: DOI

References:

[1] Balasubramaniam, P.; Abdul Samath, J.; Kumaresan, N.; Vincent Antony Kumar, A., Solution of matrix Riccati differential equation for the linear linear quadratic singular system using neural networks, Appl. Math. Comput., 182, 1832-1839 (2006) · Zbl 1107.65057
[2] Balasubramaniam, P.; Abdul Samath, J.; Kumaresan, N., Optimal control for nonlinear singular systems with quadratic performance using neural networks, Appl. Math. Comput., 187, 1535-1543 (2007) · Zbl 1114.65336
[3] Bouzerdoum, A.; Pattison, T. R., Neural networks for quadratic optimization with bound constraints, IEEE Trans. Neural Networks, 4, 293-303 (1993)
[4] Forti, M.; Tesi, A., New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuits. Syst. I, 42, 354-366 (1995) · Zbl 0849.68105
[5] Kennedy, M. P.; Chua, L. O., Neural networks for non-linear programming, IEEE Trans. Circuits. Syst., 35, 554-562 (1988)
[6] Arik, S., Global asymptotic stability of a large class of neural networks with constant time delays, Phys. Lett. A, 311, 504-511 (2003) · Zbl 1098.92501
[7] Cao, J.; Zhou, D., Stability analysis of delayed cellular neural networks, Neural Networks, 11, 1601-1605 (1998)
[8] Zhang, J., Global stability analysis in delayed cellular neural networks, Comput. Math. Appl., 45, 1707-1720 (2003) · Zbl 1045.37057
[9] Cao, J., On exponential stability and periodic solutions of CNNs with delays, Phys. Lett. A, 267, 312-318 (2000) · Zbl 1098.82615
[10] Zhang, Q.; Wei, X.; Xu, J., Global exponential convergence analysis of delayed neural networks with time varying delays, Phys. Lett. A, 318, 537-544 (2003) · Zbl 1098.82616
[11] Chen, T.; Amari, S., Stability of asymmetric Hopfield networks, IEEE Trans. Neural Networks, 12, 159-163 (2001)
[12] Forti, M.; Manetti, S.; Marini, M., A condition for global convergence of a class of symmetric neural networks, IEEE Trans. Circuits Syst., 39, 480-483 (1992) · Zbl 0775.92005
[13] Gopalsamy, K.; He, X. Z., Stability in asymmetric Hopfield nets with transmission delays, Physica D, 76, 344-358 (1994) · Zbl 0815.92001
[14] Guan, Z.; Chen, G.; Qin, Y., On equilibria, stability and instability of Hopfield neural networks, IEEE Trans. Neural Networks, 2, 534-540 (2000)
[15] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[16] Akhmetov, M. U.; Zafer, A., Stability of the zero solution of impulsive differential equation by the Lyapunov second method, J. Math. Anal. Appl., 248, 69-82 (2000) · Zbl 0965.34007
[17] Guan, Z. H.; Lam, J.; Chen, G., On impulsive autoassociative neural networks, Neural Networks, 13, 63-69 (2000)
[18] Liu, X. Zh.; Ballinger, G., Boundedness for impulsive delay differential equations and applications to population growth models, Nonlinear Anal., 53, 1041-1062 (2003) · Zbl 1037.34061
[19] Xu, D.; Yang, Zh. Ch., Impulsive delay differential inequality and stability of neural networks, J. Math. Anal. Appl., 305, 107-120 (2005) · Zbl 1091.34046
[20] Yang, Zh. Ch.; Xu, D., Stability analysis of delay neural networks with impulsive effects, IEEE Trans. Circuits Syst II: Express Briefs, 52, 517-521 (2005)
[21] Long, S.; Xu, D., Delay-dependent stability analysis for impulsive neural networks with time varying delays, Neurocomputing, 71, 1705-1713 (2008)
[22] Huang, Z.-T.; Yang, Q.-G.; Luo, X.-S., Exponential stability of impulsive neural networks with time-varying delays, Chaos Solitons Fractrals, 35, 770-780 (2008) · Zbl 1139.93353
[23] Xia, Y.; Cao, J.; Cheng, S. S., Global exponential stability of delayed cellular neural networks with impulses, Neurocomputing, 70, 2495-2501 (2007)
[24] Yang, Y.; Cao, J., Stability and periodicity in delayed cellular neural networks with impulsive effects, Nonlinear Anal. RWA, 8, 362-374 (2007) · Zbl 1115.34072
[25] Qiu, J., Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms, Neurocomputing, 70, 1102-1108 (2007)
[26] Ahmed, S.; Stamova, I. M., Global exponential stability for impulsive cellular neural networks with time-varying delays, Nonlinear Anal. TMA, 69, 786-795 (2008) · Zbl 1151.34061
[27] K. Li, Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays, Nonlinear Anal. RWA, in press (doi:10.1016/j.nonrwa.2008.08.005; K. Li, Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays, Nonlinear Anal. RWA, in press (doi:10.1016/j.nonrwa.2008.08.005
[28] Song, Q.; Zhang, J., Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays, Nonlinear Anal. RWA, 9, 500-510 (2008) · Zbl 1142.34046
[29] Zhang, Y.; Sun, J. T., Boundedness of the solutions of impulsive differential systems with time-varying delay, Appl. Math. Comput., 154, 279-288 (2004) · Zbl 1062.34091
[30] J. Cao, S. Zhong, Y. Hu, Global stability analysis for a class of neural networks with time varying delays and control input, Appl. Math. Comput. (in press); J. Cao, S. Zhong, Y. Hu, Global stability analysis for a class of neural networks with time varying delays and control input, Appl. Math. Comput. (in press) · Zbl 1128.34046
[31] Park, J. H.; Kwon, O. M.; Lee, S. M., LMI optimization approach on stability for delayed neural networks of neutral-type, Appl. Math. Comput., 196, 236-244 (2008) · Zbl 1157.34056
[32] Qiu, J.; Cao, J., Delay-dependent robust stability of neutral-type neural networks with time delays, J. Math. Control Sci. Appl., 1, 179-188 (2007) · Zbl 1170.93364
[33] H. Mai, X. Liao, C. Li, A semi-free weighting matrices approach for neutral-type delayed neural networks, J. Comput. Appl. Math., in press, (doi:10.1016/j.cam.2008.06.016; H. Mai, X. Liao, C. Li, A semi-free weighting matrices approach for neutral-type delayed neural networks, J. Comput. Appl. Math., in press, (doi:10.1016/j.cam.2008.06.016 · Zbl 1165.65039
[34] Xu, S.; Lam, J.; Ho, D. W.C.; Zou, Y., Delay-dependent exponential stability for a class of neural networks with time delays, J. Comput. Math. Appl., 183, 16-28 (2005) · Zbl 1097.34057
[35] Liu, M., Delayed standard neural network models for control systems, IEEE Trans. Neural Networks, 18, 1376-1391 (2007)
[36] Berman, A.; Plemmons, R. J., Nonnegative Matrices in Mathematical Sciences (1979), Academic Press: Academic Press New York · Zbl 0484.15016
[37] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI Control Toolbox User’s Guide (1995), The Mathworks: The Mathworks Massachusetts
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