Vector Wirtinger-type inequality and the stability analysis of delayed neural network

Communications in Nonlinear Science and Numerical Simulation

Volumn 18, Issue 5, 2013, Pages 1246-1257

  Liu, Zixin ^a,b   Yu, Jian ^a   Xu, Daoyun ^a  

^a GUIZHOU UNIVERSITY   (China)

^b GUIZHOU UNIVERSITY OF FINANCE AND ECONOMICS   (China)

Author keywords

Asymptotically stable; Characteristic equation; Delay partitioning approach; Neural network; Wirtinger type inequality

Indexed keywords

ACTIVATION ANALYSIS; CHEMICAL ACTIVATION; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; SLOPE STABILITY; STABILITY CRITERIA;

ASYMPTOTICALLY STABLE; CHARACTERISTIC EQUATION; DELAY PARTITIONING APPROACHES; DELAYED NEURAL NETWORKS; NEURAL-NETWORKS; NEURON ACTIVATION FUNCTION; NON-LINEAR NEURONS; STABILITY ANALYZE; STABILITY CRITERIONS; WIRTINGER-TYPE INEQUALITY;

NEURAL NETWORKS;

EID: 84869881881     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2012.09.027     Document Type: Article

References (28)

1. Xu X.H., Zhang J.Y., Zhang W.H. Stochastic exponential robust stability of interval neural networks with reaction-diffusion terms and mixed delays. Commun. Nonlinear Science. Nume. Simu. 2012, 17:4780-4791.
2. Cai G.L., Yao Q., Shao H.J. Global synchronization of weighted cellular neural network with time-varying coupling delays. Commun. Nonlinear Sci. Numer. Simulat. 2012, 17:3843-3847.
3. Du B.Z., Lam J. Stability analysis of static recurrent neural networks using delay-partitioning and projection. Neural Network. 2009, 22:343-347.
4. Orman Z. New sufficient conditions for global stability of neutral-type neural networks with time delays. Neurocomputing 2012, 97:141-148.
5. Kostarigka A.K., Rovithakis G.A. Adaptive dynamic output feedback neural network control of uncertain MIMO nonlinear systems with prescribed performance. IEEE Trans. Neural Network Learn. Syst. 2012, 23:138-149.
6. Balasubramaniam P., Nagamani G., Rakkiyappan R. Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun. Nonlinear Sci. Numer. Simulat. 2011, 16:4422-4437.
7. Zhang D., Yu L. Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays. Neural Network 2012, 35:103-111.
8. Tian J.K., Zhong S.M. Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components. Neurocomputing 2012, 77:114-119.
9. Hao F. Absolute stability of uncert ain discrete Lur'e systems and maximum admissible perturbed bounds. J. Franklin Inst. 2010, 347:1511-1525.
10. Mathiyalagan K., Sakthivel R., Marshal Anthoni S. Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks. Phys. Lett. A 2012, 376:901-912.
11. Phat V.N., Khongtham Y., Ratchagit K. LMI approach to exponential stability of linear systems with interval time-varying delays. Linear Algebra Appl. 2012, 436:243-251.
12. Lee S.M., Park J.H. Delay-dependent criteria for absolute stability of uncertain time-delayed Lur'e dynamical systems. J. Franklin Inst. 2010, 347:146-153.
13. Zhang Y.J., Yue D., Tian E.G. New stability criteria of neural networks with interval time-varying delay: A piecewise delay method. Appl. Math. Comput. 2009, 208:249-259.
14. Fridman E., Shaked U. control of linear state-delay descriptor systems: an LMI approach. Linear Algebra Appl. 2002, 351-352:271-302.
15. Cao J., Zhong S.M., Hu Y.Y. Delay-dependent condition for absolute stability of Lur'e control systems with multiple time delays and nonlinearities. J. Math. Anal. Appl. 2008, 338:497-504.
16. He Y., Liu G.P., Rees D. New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans. Neural Network 2007, 18:310-314.
17. He Y., et al. Stability analysis for neural networks with time-varying interval delay. IEEE T. Neural. Network 2007, 18:1850-1854.
18. Zheng C.D., Lu L.B., Wang Z.S. New LMT-based delay-dependent criterion for global asymptotic stability of cellular neural networks. Neurocomputing 2009, 72:3331-3336.
19. Tian J.K., Zhou X.B. Improved asymptotic stability criteria for neural networks with interval time-varying delay. Expert Syst. Appl. 2010, 37:7521-7525.
20. Park P.G., Ko J.W., Jeong C.K. Reciprocally convex approach to stability of systems with time-varying delays. Automatica 2011, 47:235-238.
21. Ghaoui L.E., Lebret H. Robust solutions to least squares problems with uncertain data. SIAM J. Matrix Anal. Appl. 1997, 18(4):1035-1064.
22. Gu K. An integral inequality in the stability problem of time delay systems. In: IEEE Control Systems Society and Proceedings of IEEE Conference on Decision and Control, IEEE Publisher, New York, 2000.
23. Hale JK, Verduyn Lunel SM. Introduction to functional-differential equations. In: Applied Math Sciences, vol. 99, Springer, New York, 1993.
24. Ortega J.M. Numerical analysis 1972, Academic Press, New York.
25. Li C.D., Feng G. Delay-interval-dependent stability of recurrent neural networks with time-varying delay. Neurocomputing 2009, 72:1179-1183.
26. Liu M. Delayed standard neural network model and its application. Acta Autom. Sin. 2005, 31:750-758.
27. Li T., Guo L., Sun C., Lin C. Further result on delay-dependent stability criterion of neural networks with time-varying delays. IEEE Trans. Neural Network 2008, 19:726-730.
28. Zhang H.G., et al. Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans. Neural Network 2010, 21:91-105.