Lmi-based Stability Analysis Of Delayed Cellular Neural Networks

Since cellular neural networks have been introduced by Chua and Yang, variousclasses of neural networks have been increasingly studied due to their practical impor-tance and successful applications in many areas such as communication, image process-ing, pattern recognition and so on. These applications greatly depend on the dynamicbehaviors of the underlying neural networks. Because the stability of system is the pre-condition of the design of neural networks, it is of great theoretical and practical signifi-cance to study the stability problem of neural networks. This paper is concerned with theproblem of delay-dependent stability analysis for two classes of cellular neural networkswith multiple time-varying delays. The first, based on the Lyapunov-Krasovskii stabilitytheory for functional differential equations and the linear matrix inequality approach, adelay-dependent condition for cellular neural networks with multiple time-varying delaysis obtained, which can guarantee global asymptotical stability of these networks. Com-paring with some existing results in the literature, the restriction such as the time-varyingdelays were required to be differentiable or even their time-derivatives were assumed tobe smaller than one is removed. In our result, the time-varying delays are only assumed tobe bounded. This has undoubtedly extended its application range. The second, we solvethe problem of delay-dependent stability analysis for one class of multi-delayed cellu-lar neural networks with uncertainties. Using the above results and Schur complementlemma, we get a delay-dependent condition for multi-delayed cellular neural networkswith uncertainties which can guarantee global robust stability of these networks. All ofour results in this paper are delay-dependent, so when the delays are small, the conditionswe need are looser. Moreover, because our results in this paper are all based on the LMIapproach, we can utilize Matlab's LMI Control Toolbox to verify the global stability ofcorrelation systems conveniently.