Stability And Synchronization Researches Of Markovian Jumping Neural Networks

At present, the study about the stability and synchronization of discrete recurrent neural networks has been achieved fruitful results. However, there are still some problems that have not been studied. Both in continue-time and in discrete-time neural network models with Markov jump parameters, the transition probability of Markov process is assumed to be completely known or partially unknown. And there are few articles taking the case the probability transition matrix is completely unknown into account. In fact, in practical applications, the ideal assumption of the transition probability inevitably limits the application of the results of the study in a certain extent. As far as I know, up to now, there is no relevant literature references to the analysis of stability and synchronization for discrete recurrent neural networks with both completely unknown transition probability and mixed time-varying delays. Therefore, it is meaningful and necessary to try to do the research in this area.In this paper, the stability and synchronization problems of discrete recurrent neural networks with unknown probability transition matrix and mixed timevarying delays are analyzed, and the case of completely known transition probability matrix and the case of partly unknown are considered as special cases of the unknown transition probability matrix which is studied in this paper. Firstly, the assumed condition of connection weight matrix, the driving functions, the mixed time delays and the other parameters of the discrete recurrent neural network are set up. Secondly, based on the free-weighting matrix method and the Lyapunov stability theory, the sufficient delay-dependent criterion of the stability in mean square and the synchronization in mean square of the recurrent neural networks are derived by constructing two different new Lyapunov-Krasovskii functional, using the weak infinitesimal operator, the delay piecewise idea, Kronecker product and some other matrix inequality analysis techniques. The obtained criteria are given in the form of linear matrix inequalities, which can be solved efficiently by LMI Toolbox in Matlab. Finally, numerical examples are given to verify the effectiveness and the feasibility of the stability and the synchronization criteria obtained in this paper, the hypothesis of completely unknown probability transition matrix makes the conclusion less conservative.