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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.
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
[1]Balasubramaniam, P.; Samath, J. Abdul; Kumaresan, N.; Kumar, A. Vincent Antony: 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 · doi:10.1016/j.amc.2006.06.020
[2]Balasubramaniam, P.; Samath, J. Abdul; Kumaresan, N.: Optimal control for nonlinear singular systems with quadratic performance using neural networks, Appl. math. Comput. 187, 1535-1543 (2007) · Zbl 1114.65336 · doi:10.1016/j.amc.2006.09.072
[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 · doi:10.1109/81.401145
[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 · doi:10.1016/S0375-9601(03)00569-3
[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 · doi:10.1016/S0898-1221(03)00149-4
[9]Cao, J.: On exponential stability and periodic solutions of cnns with delays, Phys. lett. A 267, 312-318 (2000) · Zbl 1098.82615 · doi:10.1016/S0375-9601(00)00136-5
[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 · doi:10.1016/j.physleta.2003.09.062
[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 · doi:10.1109/81.153645
[13]Gopalsamy, K.; He, X. Z.: Stability in asymmetric Hopfield nets with transmission delays, Physica D 76, 344-358 (1994) · Zbl 0815.92001 · doi:10.1016/0167-2789(94)90043-4
[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) · Zbl 0718.34011
[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 · doi:10.1006/jmaa.2000.6864
[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 · doi:10.1016/S0362-546X(03)00041-5
[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 · doi:10.1016/j.jmaa.2004.10.040
[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 · doi:10.1016/j.chaos.2006.05.089
[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 · doi:10.1016/j.nonrwa.2005.11.004
[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 · doi:10.1016/j.na.2008.02.067
[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)
[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 · doi:10.1016/j.nonrwa.2006.11.015
[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 · doi:10.1016/S0096-3003(03)00712-4
[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) · Zbl 1128.34046 · doi:10.1016/j.amc.2006.12.048
[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 · doi:10.1016/j.amc.2007.05.047
[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)
[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 · doi:10.1016/j.cam.2004.12.025
[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) · Zbl 0484.15016
[37]Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M.: LMI control toolbox user’s guide, (1995)