Global Stability for Stochastic Interval Neural Networks with Mixed Time Delays
The globally stochastically asymptotic stability is considered for a class of stochastic interval neural networks with mixed delays (SIDNN) in this paper, which consist of both the discrete and distributed time delays. By introducing an equivalent transformation of interval matrices, a criterion on globally stochastically asymptotic stability is established. Based on an Lyapunov function and stochastic analysis theory, a linear matrix (LMI) approach is developed to derive the sufficient condition guaranteeing the globally stochastically asymptotic stability of the equilibrium point, where the feasibility of LMIs can be easily solved by the LMI-Toolbox in Matlab, and all the delayed differential equations are calculated numerically via DDE23 Program in Matlab.
KeywordsAsymptotic Stability Robust Stability Hopfield Neural Network Stochastic Neural Network Interval Matrice
Unable to display preview. Download preview PDF.
This work was supported by Shanxi Province Science Foundation for Youths,China(No. 2010JQ1016), the Science Research Foundation of Shaanxi Province Department of Education, China(No. 2010JK560).
- 1.Hopfield J. Neurons with graded response have been collective computational properties like those of two-state neurons. Proc Nat Acad Sci USA, 81(1984)3088–3092Google Scholar
- 2.Liao X, Yu J. Robust stability for interval Hopfield neural networks with time delay. IEEE Trans Neural Networks, 9(9)(1998)1042–1046Google Scholar
- 3.Liao X, Wong K-W, Wu Z, Chen G. Novel robust stability criteria for interval-delayed Hopfield neural networks. IEEE Trans Circuits Syst I, 48(11)(2001)1355–1359Google Scholar
- 4.Chuandong Li, Jinyu Chen, Tingwen Huang. A new criterion for global stability of interval neural networks with discrete time delays. Chaos solitons and Fractals, 31(2007)561–570Google Scholar
- 5.Chuanggong Li, Jinyu Chen, A new criterion for global robust stability of interval neural networks with discrete time delays. Chaos, Solitons and Fractals, 31(2007) 561–570Google Scholar
- 6.Z. Wang et al, Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos, Solitions and Fractals, 32(2007)62–72Google Scholar
- 7.Z. Wang et al, Stability analysis of stochastic Cohen-Grossberg neural networks with mix delays. IEEE Transaction on Neural Networks, 17(2006)814–820Google Scholar