Global robust exponential stability analysis for interval recurrent neural networks

作者: Shengyuan Xu , James Lam , Daniel W.C. Ho , Yun Zou

DOI: 10.1016/J.PHYSLETA.2004.03.038

关键词: Convex optimizationCompact spaceApplied mathematicsPhysicsInterval (mathematics)Bounded functionExponential stabilityEquilibrium pointLinear matrix inequalityRecurrent neural network

摘要: This Letter investigates the problem of robust global exponential stability analysis for interval recurrent neural networks (RNNs) via linear matrix inequality (LMI) approach. The values time-invariant uncertain parameters are assumed to be bounded within given compact sets. An improved condition existence a unique equilibrium point and its RNNs with known is proposed. Based on this, sufficient obtained. Both conditions expressed in terms LMIs, which can checked easily by various recently developed convex optimization algorithms. Examples provided demonstrate reduced conservatism proposed condition.

参考文章(20)
Shengyuan Xu, Tongwen Chen, James Lam, Robust H/sup /spl infin// filtering for uncertain Markovian jump systems with mode-dependent time delays IEEE Transactions on Automatic Control. ,vol. 48, pp. 900- 907 ,(2003) , 10.1109/TAC.2003.811277
Y. S. Xia, J. Wang, On the Stability of Globally Projected Dynamical Systems Journal of Optimization Theory and Applications. ,vol. 106, pp. 129- 150 ,(2000) , 10.1023/A:1004611224835
Jinde Cao, Global stability analysis in delayed cellular neural networks. Physical Review E. ,vol. 59, pp. 5940- 5944 ,(1999) , 10.1103/PHYSREVE.59.5940
Stephen Grossberg, Nonlinear neural networks: Principles, mechanisms, and architectures Neural Networks. ,vol. 1, pp. 17- 61 ,(1988) , 10.1016/0893-6080(88)90021-4
Yau-Tarng Juang, Chin-Shen Shao, Stability analysis of dynamic interval systems International Journal of Control. ,vol. 49, pp. 1401- 1408 ,(1989) , 10.1080/00207178908559711
Charles A. Desoer, M. Vidyasagar, Feedback Systems: Input-output Properties ,(1975)
A.N. Michel, J.A. Farrell, W. Porod, Qualitative analysis of neural networks IEEE Transactions on Circuits and Systems. ,vol. 36, pp. 229- 243 ,(1989) , 10.1109/31.20200
Sanqing Hu, Jun Wang, Global exponential stability of continuous-time interval neural networks Physical Review E. ,vol. 65, pp. 036133- 036133 ,(2002) , 10.1103/PHYSREVE.65.036133
X. Xu, Impulsive control in continuous and discrete-continuous systems [Book Reviews] IEEE Transactions on Automatic Control. ,vol. 48, pp. 2288- 2289 ,(2003) , 10.1109/TAC.2003.820138