Stability Analysis of Neural Networks With Time-Varying Delay by Constructing Novel Lyapunov Functionals

作者: Tae H. Lee , Hieu M. Trinh , Ju H. Park

DOI: 10.1109/TNNLS.2017.2760979

关键词: Point (geometry)Computational complexity theoryArtificial neural networkApplied mathematicsLyapunov exponentLyapunov equationStability (learning theory)Computer scienceLyapunov redesignSymmetric matrix

摘要: This paper presents two novel Lyapunov functionals for analyzing the stability of neural networks with time-varying delay. Based on our newly proposed and a relaxed Wirtinger-based integral inequality, new criteria are derived in form linear matrix inequalities. A comprehensive comparison results is given to illustrate from both conservative computational complexity point views.

参考文章(40)
Le Van Hien, Hieu Trinh, An enhanced stability criterion for time-delay systems via a new bounding technique Journal of The Franklin Institute-engineering and Applied Mathematics. ,vol. 352, pp. 4407- 4422 ,(2015) , 10.1016/J.JFRANKLIN.2015.06.023
Hong-Bing Zeng, Yong He, Min Wu, Jinhua She, New results on stability analysis for systems with discrete distributed delay Automatica. ,vol. 60, pp. 189- 192 ,(2015) , 10.1016/J.AUTOMATICA.2015.07.017
Tae H. Lee, Ju H. Park, Myeong-Jin Park, Oh-Min Kwon, Ho-Youl Jung, On stability criteria for neural networks with time-varying delay using Wirtinger-based multiple integral inequality Journal of the Franklin Institute. ,vol. 352, pp. 5627- 5645 ,(2015) , 10.1016/J.JFRANKLIN.2015.08.024
Jie Chen, Vladimir Kharitonov, Kequin Gu, Stability of Time-Delay Systems ,(2003)
A. Cochocki, Rolf Unbehauen, Neural networks for optimization and signal processing ,(1993)
PooGyeon Park, Won Il Lee, Seok Young Lee, Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems Journal of the Franklin Institute. ,vol. 352, pp. 1378- 1396 ,(2015) , 10.1016/J.JFRANKLIN.2015.01.004
O.M. Kwon, Ju H. Park, S.M. Lee, E.J. Cha, Analysis on delay-dependent stability for neural networks with time-varying delays Neurocomputing. ,vol. 103, pp. 114- 120 ,(2013) , 10.1016/J.NEUCOM.2012.09.012
Hong-Bing Zeng, Yong He, Min Wu, Jinhua She, Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay IEEE Transactions on Automatic Control. ,vol. 60, pp. 2768- 2772 ,(2015) , 10.1109/TAC.2015.2404271