Robust Stability Criterion for Delayed Neural Networks with Discontinuous Activation Functions
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Abstract
The problem of global robust stability for a class of uncertain delayed neural networks with discontinuous activation functions has been discussed. The uncertainty is assumed to be of norm-bounded form. Based on Lyapunov–Krasovskii stability theory as well as Filippov theory, the conditions are expressed in terms of linear matrix inequality, which make them computationally efficient and flexible. An illustrative numerical example is also given to show the applicability and effectiveness of the proposed results.
Keywords
Delayed neural network Global stability Linear matrix inequality Discontinuous neuron activations Norm-bounded uncertainPreview
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References
- 1.Zhu W, Hu J (2006) Stability analysis of stochastic delayed cellular neural networks by LMI approach. Chaos Solitons Fractals 29(1): 171–174MATHCrossRefMathSciNetGoogle Scholar
- 2.Li P, Cao J (2006) Stability in static delayed neural networks: a nonlinear measure approach. Neurocomputing 69(15): 1776–1781CrossRefMathSciNetGoogle Scholar
- 3.Singh V (2007) Global robust stability of delayed neural networks: estimating upper limit of norm of delayed connection weight matrix. Chaos Soliton Fractals 32(1): 259–263MATHCrossRefGoogle Scholar
- 4.Wang Z, Liu Y, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356(4): 346–352CrossRefGoogle Scholar
- 5.Zhang Q, Wei X, Xu J (2007) A new global stability result for delayed neural networks. Nonlinear Anal Real World Appl 8(3): 1024–1028MATHCrossRefMathSciNetGoogle Scholar
- 6.Lu W, Rong L, Chen T (2003) Global convergence of delayed neural network systems. Int J Neural Syst 13(3): 1–12CrossRefGoogle Scholar
- 7.Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst I, Fundam Theory Appl 50(11): 1421–1435CrossRefMathSciNetGoogle Scholar
- 8.Forti M, Nistri P, Papini D (2005) Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans Neural Netws 16(6): 1449–1463CrossRefGoogle Scholar
- 9.Forti M, Grazzini M, Nistri P, Pancioni L (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. IEEE Trans Neural Netw 214(6): 88–99MATHMathSciNetGoogle Scholar
- 10.Papini D, Taddei V (2005) Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations. Phys Lett A 343(2): 117–128MATHCrossRefGoogle Scholar
- 11.Lu W, Chen T (2005) Dynamical behaviors of Cohen–Grossberg neural networks with discontinuous activation functions. Neural Netw 18(3): 231–242MATHCrossRefGoogle Scholar
- 12.Lu W, Chen T (2006) Dynamical behaviors of delayed neural network systems with discontinuous activation functions. Neural Comput 18(1): 683–708MATHCrossRefMathSciNetGoogle Scholar
- 13.Lu W, Chen T (2008) Almost periodic dynamics of a class of delayed neural networks with discontinuous activation. Neural Comput 20(4): 1065–1090MATHCrossRefMathSciNetGoogle Scholar
- 14.Qi H (2006) New sufficient conditions for global robust stability of delayed neural networks. IEEE Trans Circuits Syst 1, Regul Pap 18(1): 683–708Google Scholar
- 15.Singh V (2007) Novel LMI condition for global robust stability of delayed neural networks. Chaos Soliton Fractals 34(4): 503–508 (in press)MATHCrossRefGoogle Scholar
- 16.Singh V Novel global robust stability criterion for neural networks with delay. Chaos Solitons Fractals, doi: 10.1016/j.chaos.2008.01.001
- 17.Qi H (2003) Global robust stability of delayed neural networks. IEEE Trans Circuits Syst I, Fundam Theory Appls 50(1): 156–160CrossRefGoogle Scholar
- 18.Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I, Regul Pap 52(3): 417–426MathSciNetGoogle Scholar
- 19.Zuo Z, Wang Y (2007) Robust stability criterion for delayed cellular neural networks with norm-bounded uncertainties. IEE Proc Control Theory Appl 1(1): 387–392CrossRefMathSciNetGoogle Scholar
- 20.Singh V (2007) LMI approach to the global robust stability of a larger class of neural networks with delay. Chaos Solitons Fractals 32(4): 1927–1934MATHCrossRefMathSciNetGoogle Scholar
- 21.Singh V (2004) Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proc Control Theory Appl 151(1): 125–129CrossRefGoogle Scholar
- 22.Xu S, Lam J, Ho D, Zou Y (2005) Improved global robust asymptotic stability criteria for delayed cellular neural networks. IEEE Trans Syst Man Cybern B Cybern 35(6): 1317–1321CrossRefGoogle Scholar
- 23.Kwon O, Park J, Lee S (2008) On robust stability for uncertain neural networks with interval time-varying delays. IET Control Theory Appl 2(7): 625–634CrossRefMathSciNetGoogle Scholar
- 24.Xie L, Fu M, Souza D (1992) H ∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Trans Automat Contr 37(8): 1253–1256CrossRefGoogle Scholar
- 25.Filippov A (1988) Differential equations with discontinuous right-hand side. Kluwers, BostonGoogle Scholar
- 26.Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, HiladelphiaMATHGoogle Scholar
- 27.Aubin J, Cellina A (1984) Differential inclusions. Springer, BerlinMATHGoogle Scholar
- 28.Clarke F (1994) Optimization and nonsmooth analysis. Wiley, New YorkGoogle Scholar
- 29.Baciotti A, Conti R, Marcellini P (2000) Discontinuous ordinary differential equations and stabilization. Universita di Firenze, ItalyGoogle Scholar
- 30.Hale J (1994) Ordinary differential equations. Wiley, New YorkGoogle Scholar
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