Some improved methods to analysis stability of recurrent neural networks with interval time-varying delays

References

• Y.Q. Bai and J. Chen, New stability criteria for recurrent neural networks with interval time-varying delay, Neurocomputing 121 (2013), pp. 179–184. doi: 10.1016/j.neucom.2013.04.031
   Web of Science ®Google Scholar
• P. Balasubramaniam and S. Lakshmanan, Delay-range dependent stability criteria for neural networks with Markovian jumping parameters, Nonlinear Anal. Hybrid Syst. 3 (2009), pp. 749–56. doi: 10.1016/j.nahs.2009.06.012
   Web of Science ®Google Scholar
• P. Balasubramaniam, S. Lakshmanan, and R. Rakkiyappan, Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties, Neurocomputing 72 (2009), pp. 3675–3682. doi: 10.1016/j.neucom.2009.06.006
   Web of Science ®Google Scholar
• P. Balasubramaniam, V. Vembarasan, and R. Rakkiyappan, Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term, Neural Comput. Appl. 21 (2012), pp. 1593–616. doi: 10.1007/s00521-011-0639-x
   Web of Science ®Google Scholar
• J. Cao and J. Wang, Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I Reg. Papers 52 (2005), pp. 417–426. doi: 10.1109/TCSI.2004.841574
   Web of Science ®Google Scholar
• K. Gu, An integral inequality in the stability problem of time-delay systems, Proceedings of the IEEE Conference on Decision and Control 3 (2000), pp. 2805–2810.
   Google Scholar
• Y. He, M. Wu, J.H. She, and G.P. Liu, Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Syst. Control Lett. 51 (2004), pp. 57–75. doi: 10.1016/S0167-6911(03)00207-X
   Web of Science ®Google Scholar
• L. Hu, H. Gao, and W.X. Zheng, Novel stability of cellular neural networks with interval time-varying delay, Neural Netw. 21 (2008), pp. 1458–1463. doi: 10.1016/j.neunet.2008.09.002
   PubMed Web of Science ®Google Scholar
• M.D. Ji, Y. He, C.K. Zhang, and M. Wu, Novel stability criteria for recurrent neural networks with time-varying delay, Neurocomputing 138 (2014), pp. 383–391. doi: 10.1016/j.neucom.2014.01.024
   Web of Science ®Google Scholar
• O.M. Kwon, S.M. Lee, J.H. Park, and E.J. Cha, New approaches on stability criteria for neural networks with interval time-varying delays, Appl. Math. Comput. 213 (2012), pp. 9953–64.
   Google Scholar
• O.M. Kwon, J.H. Park, S.M. Lee, and E.J. Cha, Analysis on delay-dependent stability for neural networks with time-varying delays, Neurocomputing 103 (2013), pp. 114–120. doi: 10.1016/j.neucom.2012.09.012
   Web of Science ®Google Scholar
• O.M. Kwon, M.J. Park, S.M. Lee, J.H. Park, and E.J. Cha, Stability for neural networks with time-varying delays via some new approaches, IEEE Trans. Neural Netw. Learn Syst. 24 (2013), pp. 181–193. doi: 10.1109/TNNLS.2012.2224883
   PubMed Web of Science ®Google Scholar
• O.M. Kwon, M.J. Park, J.H. Park, S.M. Lee, and E.J. Cha, New and improved results on stability of static neural networks with interval time-varying delays, Appl. Math. Comput. 239 (2014), pp. 346–357.
   Web of Science ®Google Scholar
• S. Lakshmanan, V. Vembarasan, and P. Balasubramaniam, Delay decomposition approach to state estimation of neural networks with mixed time-varying delays and Markovian jumping parameters, Math. Methods Appl. Sci. 36 (2013), pp. 395–412. doi: 10.1002/mma.2597
   Web of Science ®Google Scholar
• W.I. Lee, S.Y. Lee, and P.G. Park, Improved stability criteria for recurrent neural networks with interval time-varying delays via new Lyapunov functional, Neurocomputing 155 (2015), pp. 128–134. doi: 10.1016/j.neucom.2014.12.040
   Web of Science ®Google Scholar
• C. Li and G. Feng, Delay-interval-dependent stability of recurrent neural networks with time-varying delay, Neurocomputing 72 (2009), pp. 1179–1183. doi: 10.1016/j.neucom.2008.02.011
   Web of Science ®Google Scholar
• T. Li, A. Song, S. Fei, and T. Wang, Delay-derivative-dependent stability for delayed neural networks with unbounded distributed delay, IEEE Trans. Neural Netw. 21 (2010), pp. 1365–1371. doi: 10.1109/TNN.2010.2051455
   PubMed Web of Science ®Google Scholar
• T. Li, A. Song, M. Xue, and H. Zhang, Stability analysis on delayed neural networks based on an improved delay-partitioning approach, J. Comput. Appl. Math. 235 (2011), pp. 3086–3095. doi: 10.1016/j.cam.2010.10.002
   Web of Science ®Google Scholar
• T. Li, T. Wang, A. Song, and S. Fei, Combined convex technique on delay-dependent stability for delayed neural networks, IEEE Trans. Neural Netw. Learn. Syst. 24 (2013), pp. 1459–1466. doi: 10.1109/TNNLS.2013.2256796
   PubMed Web of Science ®Google Scholar
• T. Li and X.L. Ye, Improved stability criteria of neural networks with time-varying delays: An augmented LKF approach, Neurocomputing 73 (2010), pp. 1038–1047. doi: 10.1016/j.neucom.2009.10.001
   Web of Science ®Google Scholar
• J. Liang and J.D. Cao, Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays, Phys. Lett. A 314 (2003), pp. 434–442. doi: 10.1016/S0375-9601(03)00945-9
   Web of Science ®Google Scholar
• J. Liang and J. Cao, A based-on LMI stability criterion for delayed recurrent neural networks, Chaos Solitons Fractals 28 (2006), pp. 154–160. doi: 10.1016/j.chaos.2005.04.120
   Web of Science ®Google Scholar
• G.P. Liu, Nonlinear Identification and Control: A Neural Network Approach, Springer/Wiley, London/York, 2001.
   Google Scholar
• Z. Liu, J. Yu, and D. Xu, Vector writinger-type inequality and the stability analysis of delayed neural network, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), pp. 1247–1257.
   Web of Science ®Google Scholar
• D.P. Mandic and J.A. Chambers, Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures, and Stability, Wiley, New York, 2001.
   Google Scholar
• P.G. Park, A delay-dependent stability criterion for systems with uncertain linear state-delayed systems, IEEE Trans. Autom. Control 35 (1999), pp. 876–877. doi: 10.1109/9.754838
   Web of Science ®Google Scholar
• P.G. Park, J.W. Ko, and C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica 47 (2011), pp. 235–238. doi: 10.1016/j.automatica.2010.10.014
   Web of Science ®Google Scholar
• A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems, Automatica 49 (2013), pp. 2860–2866. doi: 10.1016/j.automatica.2013.05.030
   Web of Science ®Google Scholar
• H. Shao, Delay-dependent stability for recurrent neural networks with time-varying delays, IEEE Trans. Neural Netw. 19 (2008), pp. 1647–1651. doi: 10.1109/TNN.2008.2001265
   PubMed Web of Science ®Google Scholar
• R.E. Skelton, T. Iwasaki, and K.M. Grigoradis, A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, New York, 1997.
   Google Scholar
• Q. Song, J.D. Cao, and Z. Zhao, Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays, Nonlinear Anal. Real World Appl. 7 (2006), pp. 65–80. doi: 10.1016/j.nonrwa.2005.01.004
   Web of Science ®Google Scholar
• J. Sun and J. Chen, Stability analysis of static recurrent neural network s with interval time-varying delay, Appl. Math. Comput. 221 (2013), pp. 111–120.
   Web of Science ®Google Scholar
• Y. Wang, C. Yang, and Z. Zuo, On exponential stability analysis for neural networks with time-varying delays and general activation functions, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), pp. 1447–1459. doi: 10.1016/j.cnsns.2011.08.016
   Web of Science ®Google Scholar
• Z.G. Wu, J. Lam, H. Su, and J. Chu, Stability and dissipativity analysis of static neural networks with time delay, IEEE Trans. Neural Networks 23 (2012), pp. 199–210. doi: 10.1109/TNNLS.2011.2178563
   PubMed Web of Science ®Google Scholar
• D.S. Yang, X.R. Liu, Y.K. Xu, Y.C. Wang, and Z.B. Liu, State estimation of recurrent neural networks with interval time-varying delay: An improved delay-dependent approach, Neural Comput. Appl. 23 (2013), pp. 1149–1158. doi: 10.1007/s00521-012-1061-8
   Web of Science ®Google Scholar
• Q. Yang, Q. Ren, and X. Xie, New delay dependent stability criteria for recurrent neural networks with interval time-varying delay, ISA Trans. 53 (2014), pp. 994–999. doi: 10.1016/j.isatra.2014.05.009
   PubMed Web of Science ®Google Scholar
• B. Yang, L. Wang, C.X. Fan, and M. Han, New delay-dependent stability criteria for networks with time-varying delays, American Control Conference, Portland, Oregon, USA, 2014, 2881–2886.
   Google Scholar
• H.B. Zeng, Y. He, M. Wu, and J. She, Free-matrix-based integral integral inequality for stability analysis of systems with time-varying delay, IEEE Trans. Autom. Control 60(10) (2015), pp. 2768–2772. doi: 10.1109/TAC.2015.2404271
   Web of Science ®Google Scholar
• X.M. Zhang and Q.L. Han, Global asymptotic stability for a class of generalized neural networks with interval time-varying delays, IEEE Trans. Neural Netw. 22(8) (2011), pp. 1180–1192. doi: 10.1109/TNN.2011.2147331
   PubMed Web of Science ®Google Scholar
• C.K. Zhang, Y. He, L. Jiang, Q.H. Wu, and M. Wu, Delay-dependent stability criteria for generalized neural networks with two delay components, IEEE Trans. Neural Netw. Learn. Syst. 25(7) (2014), pp. 1263–1276. doi: 10.1109/TNNLS.2013.2284968
   Web of Science ®Google Scholar
• H.G. Zhang, Z.W. Liu, G.B. Huang, and Z.S. Wang, Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay, IEEE Trans. Neural Netw. 21 (2010), pp. 91–106. doi: 10.1109/TNN.2009.2034742
   PubMed Web of Science ®Google Scholar
• Y. Zhang, D. Yue, and E. Tian, New stability criteria of neural networks with interval time-varying delays: A piecewise delay method, Appl. Math. Comput. 208 (2009), pp. 249–259.
   Web of Science ®Google Scholar
• Z. Zuo, C. Yang, and Y. Wang, A new method for stability analysis of recurrent neural networks with interval time-varying delay, IEEE Trans. Neural Netw. 21 (2010), pp. 339–344. doi: 10.1109/TNN.2009.2037893
   PubMed Web of Science ®Google Scholar