Stability Analysis For Interval Neural Networks With Delays

Artificial neural network is an active marginal interdisciplinary subject. It is a hotspots about the research and application of artificial intelligence, cognitive science,nonlinear dynamics and related profession. In practice, time delays and parameterperturbation inevitably exist, which is frequently a source of instability in system. Itbecomes a very important research subject to research the stability of time delayed intervalneural network.The time-delay interval neural network were studied mainly ranging from theparameter uncertainties, mixed time delays, nonsmooth functions and switching rules.Main work is as follows:Firstly, the robust stability problem of a class of BAM neural network with timedelays in parameter uncertainty is studied. By exploiting the theory of homeomorphismmapping, norm inequalities techniques and constructing a suitable Lyapunov function,some sufficient conditions are derived for the existence, uniqueness and global asymptoticstability of the equilibrium point. The example shows the validity and feasibility for theproposed criteria. This paper provides a useful reference for the studying of interval BAMneural network systems.Secondly, the robust exponential stability issue for the interval Cohen-Grossberg typeBAM neural networks with nonsmooth behaved functions and mixed time delays isinvestigated. Based on homeomorphism mapping theory and nonsmooth analysisapproach, the existence and uniqueness of the equilibrium point are proved. By applyinglinear matrix inequality (LMI), free-weighting matrix technique, and available Lyapunovfunctional method, some delay dependent conditions are achieved in terms of LMIs toensure the considered neural network to be globally robustly exponentially stable. Theresults obtained in this paper are little conservative compared with the previous results inthe literature. Finally, two simulation examples are given to illustrate the validity of thetheoretical results.Thirdly, we analyze the robust stability of the interval switched neural network, relying on switched rule, the condition are proposed to guarantee the interval CohenGrossberg type BAM neural network with mixed delays and switch robustly exponentiallystable. Moreover, the delay-dependent criterion is achieved in terms of linear matrixinequalities (LMIs).