Unknown Probability Transfer Rate And Mixed Time Delay And Synchronicity Analysis The Stability Of The Discrete Neural Networks

In this paper, the Stability analysis and Synchronization of a class of discrete-time stochastic Bi-direction associative memory (BAM) neural networks with mode-dependentdelay and partly unknown transition probabilities are investigated. The considered systems are more general than the systems with completely known or completely unknown transition probabilities, which can be viewed as two special cases of the tackled here. We aim to establish easily verifiable conditions under which the transition probabilities are partly unknown in the mean square. By employing new Lyapunov-Krasovskii functions combining with the delay partitioning technique and the free-weighting matrix and conducting stochastic analysis, several linear matrixes (LMIs) approach is developed to derive the criteria for the asymptotic stability, which cab be expressed in form of LMIs and can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox, the new criterion proves to be less conservative. It is worth mentioning that the so-called sector-condition assumptions made on the activation functions in this paper is more general than the usual Lipschiz conditions, and the criteria derived are dependent on both the discrete time delay and distributed time delay, and are therefore less conservative. Finally, two simple examples are provided to demonstrate the effectiveness and applicability of the proposed testing criteria, and the numerical simulations further confirm our theoretical results.The thesis falls into three parts. The opening section gives an introduction to the related background, and states the significance and the latest progress in the Stability and Synchronization analysis problems for BAM neural networks. We conclude this paper with the formulation of problems to be investigated.In chapter2, we deal with the stability analysis problem of the addressed neural network. By constructing a new Lyapunov-Krasovskii function, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time BAM neural networks to be globally asymptotically stable. And a numerical example is presented to illustrate the usefulness and effectiveness of the main results obtained.In chapter3, we turn to the synchronization among an array of identical coupled Markovian jump BAM neural networks with partly unknown transition probabilities. By utilizing the Lyapunov stability theory and the kronecket product, it is shown that the addressed synchronization problem is solved if several LMIs are feasible. All the conditions obtained are expressed in the terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. An example is given for illustrative purpose.