Novel Stability Condition Of Stochastic Fuzzy Neural Networks With Markovian Jumping Under Impulsive Perturbations

To some extent,vagueness can't be avoided in the human way of regarding the world.In fact,vague notations are usually used to explain some extensive detailed descriptions.It is interesting and important to study the stability of fuzzy neural networks.Because the fuzzy neural network is a cornerstone in image processing and pattern recognition.As is well known,noise or impulsive disturbances are major sources for causing instability in neural networks.Therefore,noise or impulsive disturbances should be taken into account when studying the stability of fuzzy neural networks,and the corresponding fuzzy nerual networks with noise and impulsive disturbances are called stochastic fuzzy neural networks or fuzzy impulsive neural networks.To the best of our knowledge,there have no papers reported to study the stability of fuzzy neural networks with Markovian jumping under impulsive perturbations.This paper investigates the global asymptotic stability of fuzzy neural networks with maxed delays and Markovian jumping under impulsive perturbations in mean square.Chapter 1 is an introduction,mainly on the background of fuzzy neural networks and the meaning of the stability,the model of fuzzy neural networks with Markovian jumping under impulsive perturbations,the stability theory of dynamical systems,and then describes the main work of this paper.Chapter 2,By using stochastic analysis method,linear convex combination technique,Jensen integral inequality and the free-weight matrix method,a novel sufficient condition is derived to ensure the global asymptotic stability of the equilibrium point of the considered networks in mean square.Finally,a numerical example is given to demonstrate the effectiveness via Matlab software.