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Exponential Stability Analysis For Switched Cellular Neural Networks With Time-Varying Delays And Impulsive Effects

Authors: Zixin Liu; Fangwei Chen;

Exponential Stability Analysis For Switched Cellular Neural Networks With Time-Varying Delays And Impulsive Effects

Abstract

{"references": ["L. Chua, L. Yang, Cellular neural networks: Theory, IEEE Trans. Circuits\nSyst, 35 (1988) 1257-1272.", "Q. Wang, X. Liu, Exponential stability of impulsive cellular neural\nnetworks with time delay via Lyapunov functionals, Applied Mathematics\nand Computation, 194 (2007) 186-198.", "H. Wang, X. Liao, and C. Li, Existence and exponential stability of\nperiodic solution of BAM neural networks with impulse and time-varying\ndelay, Chaos, Solitons & Fractals, 33 (2007) 1028-1039.", "S. Mohamad, Exponential stability in Hopfield-type neural networks with\nimpulses, Chaos, Solitons & Fractals, 32 (2007) 456-467.", "Z. Huang, X. Luo, Q. Yang, Global asymptotic stability analysis of\nbidirectional associative memory neural networks with distributed delays\nand impulse, Chaos, Solitons & Fractals, 34 (2007) 878-885.", "Y. Li, W. Xing, and L. Lu, Existence and global exponential stability\nof periodic solution of a class of neural networks with impulses, Chaos,\nSolitons & Fractals, 27 (2006) 437-445.", "J. Mancilla-Aguilar, R. Garciaa, An extension of LaSalles invariance\nprinciple for switched systems, Systems and Control Letters, 55 (2006)\n376- 384.", "W. Feng, J. Zhang, Stability analysis and stabilization control of multivariable\nswitched stochastic systems, Automatica, 42 (2006) 169-176.", "N. ElFarra, P. Mhaskar, and P. Christofides, Output feedback control of\nswitched nonlinear systems using multiple Lyapunov functions,Systems\nand Control Letters, 54 (2005) 1163-182.\n[10] G. Hu, On stability of switched homogeneous nonlinear systems, J. Math.\nAnal. Appl, 334 (2007) 414-430.\n[11] M. Sen, Quadratic stability and stabilization of switched dynamic systems\nwith un-commensurate internal point delays, Applied Mathematics\nand Computation, 185 (2007) 508-526.\n[12] F. Cao, Neural Networks with Single Hidden Layer and the Best\nPolynomial Approximation, ACTA MATHEMATICA SINICA, Chinese\nSeries, 50 (2007) 385-392.\n[13] F. Cao, Y. Zhang, Interpolation and Approximation by Neural Networks\nin Distance Space, ACTA MATHEMATICA SINICA, Chinese Series, ,51\n(2008) 91-98."]}

In this Letter, a class of impulsive switched cellular neural networks with time-varying delays is investigated. At the same time, parametric uncertainties assumed to be norm bounded are considered. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions guaranteeing exponential stability for all admissible parametric uncertainties are derived via constructing appropriate Lyapunov functional. One numerical example is provided to illustrate the validity of the main results obtained in this paper.

Keywords

cellular neural networks., exponential stability, Switched systems

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