Stability Criteria for Uncertainty Markovian Jumping Parameters of BAM Neural Networks with Leakage and Discrete Delays

Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, one numerical example is given to illustrate the the usefulness and feasibility of the proposed main results.

Keywords: Stability, Markovian jumping neural networks, Timevarying delays, Linear matrix inequality.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091322

References:

[1] Y.H.Du, S.M.Zhong, N.Zhou, L.Nie, W.Q.Wang, Exponential passivity of BAM neural networks with time-varying delays. Applied Mathematics and Computation 221 (2013) 727-740.
[2] H.W.Wang,Q.K.Song,C.G.Duan,LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions, Math.Comput.Simul. 81 (2010) 837-850.
[3] Yang,R,Gao,H,Shi,P.Novel robust stability criteria for stochastic Hopfield neural networks with time delays.IEEE Transactions on Systems,Man and Cybernetics,Part B,(39)2,(2009)467-474.
[4] H. D. Qi, L. Qi, Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis, IEEE Trans. Neural Netw., 2004, 15(1), pp. 99-109.
[5] H. Ye, N. Micheal, K. Wang, Robust stability of nonlinear time-delay systems with applications to neural networks, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 1996, 43(7), pp. 532-543.
[6] Y.Ou, H.Liu, Y.Si, Z.Feng, Stability analysis of discrete-time stochastic neural networks with time-varying delay, Neurocomputing, 72 (2010) 740-748.
[7] Liu PL. Robust exponential stability for uncertain time-varying delay systems with delay dependence.Journal of The Franklin Institute 2009;346(10):958-968.
[8] Y. Liu, Z. Wang, and X. Liu, On global exponential stability of generalized stochastic neural networks with mixed time-delays, Neurocomputing, 2006, 70(1-3), pp. 314-326, Dec. 2006.
[9] S. Arik,Global asymptotic stability of hybrid bidirectional associative memory neural networks with time delays. Phys. Lett.A 351(2006) 85-91.
[10] Q.K. Song, Z.J. Zhao, Y.M. Li, Global exponential stability of BAM neural networks with distributed delays and reaction diffusion terms, Phys. Lett.A 335(2005) 213-225.
[11] J.H.Park,O.M.Kwon,Further results on state estimation for neural networks of neutral-type with time-varying delay,App. Math.. Comput. 208(2009) 69-57.
[12] Z.G.Wu, P.Shi, H.Su, J.Chu, Delay-dependent stability analysis for switched neural networks with time-varying delay,IEEE Trans. Syst.Man Cybern. Part B: Cybern, 41 (6) (2011) 1522-1530.
[13] J.K.Tian, S.M.Zhong, Improved delay-dependent stability for neural networks with time-varying delay, Appl.Math.Comput. 217 (2011) 10278- 10288.
[14] Q. Zhang, X. Wei, and J. Xu, Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos, Solitons Fractals, 2005, 23(4), pp. 1363-1369.
[15] K. Gu, V. K. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Boston, MA: Birkhauser, 2003.
[16] M.S.Mahmoud, P.Shi, Robust stability,stabilization and H∞ control of time-delay systems with Markovian jump parameters,Int.J. Robust Nonlinear Control 13(2003)755-784.
[17] O.M.Kwon, J.H.Park, Improved delay-dependent stability criterion for networks with time-varying, Phys Lett. A 373(2009) 529-535.
[18] X.F. Liao, G. Chen, E.N.Sanchez, Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Netw. 15(2002) 855-866.
[19] P. Park, J. W. Ko, and C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 2011, 47(1), pp. 235-238.
[20] L.Xie,Stochastic robust stability analysis for Markovian jumping neural networks with delays,in:Proceedings IEEE International Conferences on Networking, Sensing and Control,vol. 22,2005,pp. 923-928.
[21] Z.Wang, Y.Liu,X.Liu,State estimation for jumping recurrent neural networks with discrete and distributed delays, Neural Netw. 22(2009)41- 48.
[22] X.Lou, B.Cui,Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump paramters, J.Math. Anal. Appl. 328(2007)316-326.
[23] K.Gu,An integral inequality in the stability problem of time delay systems, in: Proceedings of the 39th IEEE Conference on Decision Control,2000,pp.2805-2810.
[24] H.Liu, Y.Ou, J.Hu, T.Liu, Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jump paramters, Neural Netw.23(2010)315-321.
[25] K.Gopalsamy, Leakage delay in BAM,J.Math. Anal. 325(2007)1117- 1132.
[26] S.Peng, Global attractive periodic solutions of BAM neural networks with continously distributed delays in the leakage terms, Nonlinear Anal. Real World Appl.11(2010)2141-2151.
[27] H.Bao, J.Cao, Stochastic global exponential for neutral-type impulsive impilsive neural networks with mixed time-delays and Markovian jumping paramters. Commun. Nonlinear Sci.Numer.Simul. 16(2011)3786-3791.
[28] W.Han, Y.Liu, L.Wang, Robust exponential stability of Markovian jumping neural networks with mode-dependent delay,Commun.Nonlinear Sci Numer.Simul 15(2010)2529-2535.