DISCRETE – TIME RECURRENT NEURAL NETWORKS WITH TIME - VARYING DELAYS AND MARKOVIAN PARAMETER:EXPONENTIAL STABILITY ANALYSIS

Mathematics

This paper is concerned with the analysis of exponential stability for a class of discrete time recurrent neural network with time varying delay and time delay.For the former the activation function is more general than the recently commonly used Lipschitz conditions. Under such mild conditions we prove the existence of the equilibrium point.Then by employing a Lyapunov – Krasovskii functional, a unfied Linear Matrix Inequality(LMI) is developed to establish sufficient conditions for DRNN to be globally exponentially stable. For the latter the stability is analysed with time delays and Markovian jumping parameters. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is exponentially stable independent of the time delays.Then by employing Lyapunov –Krasovskii, LMI approach is developed to verify the exponential stability

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