Dynamic Behavoiurs of Delayed Recurrent Neural Networks with Stochastic Perturbation and Markovian Jumping Parameters Stability

Abstract

Neural Networks NN is a computing system made up of a number of simple highly interconnected processing elements which process information by their dynamic state response to external inputs The study of neural networks have been widely applied successfully in signal processing automatic control classification knowledge acquisition pattern recognition combinatorial optimization machine learning and other fields In this thesis Linear Matrix Inequality LMI newlineoptimization technique to new stability results with discrete interval and distributed timevarying delays for Stochastic Neural Networks SNN is derived The sufficient conditions are derived for the newlineglobal exponential stability of stochastic CohenGrossberg neural networks with multiple timevarying delays by using LMI approach In addition to this the delayprobability distribution dependent robust stability problem for a class of uncertain Markovian jump stochastic neural networks with timevarying delays has been investigated The information of probability distribution of the time delay is considered and transformed into parameter matrices of the transferred stochastic neutral networks model Based on the Lyapunov Krasovskii functional and stochastic analysis approach a novel delayprobability distribution dependent sufficient condition is obtained in the LMI form such that delayed Markovian jump stochastic neural networks are robustly globally asymptotically stable in the mean square for all admissible uncertainties An important feature of the result is that the stability conditions newlineare dependent on the probability distribution of delays and upper bound of the derivative is allowed to be greater than or equal to 1 The passivity analysis of Markovian jumping neural networks with newlineleakage time varying delays are studied Based on a Lyapunov functional that accounts for the mixed time delays a leakage delaydependent passivity conditions are derived in terms of LMIs The mixed delays includes leakage time varying delays discrete timevarying delays and distributed timevarying