Stability Analysis Of A Class Of Recurrent Neural Network Model

In recent years, the study of dynamical behaviors of recurrently connected neuralnetworks has attracted more and more researchers for their successful application in di?er-ent areas such as pattern recognition, associate memory, and combinatorial optimization.According to whether neuron states(the external states of neurons)or local fields states(theinternal states of neurons)are taken as basic variables, neural networks can be classifiedas static neural networks or local field neural networks. The recurrent back-propagationneural networks given below are static neural networks.In this paper, we analyze the dynamical behaviors of the recurrent back-propagationneural networks, especially the global stability and robust stability. The main contentconcerns the analysis for the globally robust exponential stability of the recurrent back-propagation neural network, which is independent of the delays; the analysis for the globalrobust asymptotic stability and the global robust exponential stability for the delayedrecurrent neural network; the investigation on the global exponential stability and theglobal robust exponential stability for the expanded recurrent neural network, which isdependent of the delays.The paper has four parts.In the first chapter, the background, the necessity and the development for thestudy of neural networks are presented. Then, some basic theories used in the chaptersare outlined. And the main work of this paper is also simply introduced.In the second chapter, firstly several preliminary comparisons about the Hopfieldnetwork and the recurrent back-propagation network are introduced. Then the criterionof the global exponential stability for the recurrent back-propagation network is givenvia the method of linear matrix inequality and the Lyapunov-Krasovskii function. Onthe base of this result, through conversion of matrix and variety of parameters, we get aconclusion that the network is the global robust exponential stable.In the third chapter, the delay has been added to the network that studied in thesecond chapter. With linear matrix inequalities and the Lyapunov-Krasovskii functions,the global robust asymptotic stability and the global robust exponential stability for thedelayed recurrent neural network are analyzed respectively.In the fourth chapter, combining the characters of the two models, we give a ex-panded recurrent neural network model. Then the global stability for its is analyzed bymatrix measures approach, the Lyapunov-Krasovskii function and the delayed di?eren-tial inequality. Also, several criterions are given in terms of matrix inequalities and theLyapunov-Krasovskii function, for checking the global robust exponential stability for the expanded recurrent neural network.