Two Researches On Stability Analysis Of Neural Networks With Impulsive Effect

This article focuses on stability analysis of two classes of Neural Networks with time-varying delay and impulsive effect.One is stability of complex-valued neural networks with both time-vary delays and impulsive effects,the other is stochastic stability for neutral-type impulsive neural networks with mixed time-delays and Markovian jumping parameters.By constructing two different Lyapunov-Krasovskii functional,using Jensen integral inequality,Lipschitz continuity conditions,methods of Schur complement lemma,we obtained the sufficient condition for stability.In Chapter 1,the background of Neural Networks,the research status of neural network with time-varying delay,impulse effect neural network and neutral neural network and the main contents of this paper are introduced.In Chapter 2,the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed.By employing Lyapunov functional method and using matrix inequality technique,several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence,uniqueness and global exponential stability of equilibrium point for the considered neural networks.In Chapter 3,the asymptotic stability for neutral-type neural networks with discrete and unbounded distributed time-varying delays and Markovian jumping parameters under impulsive perturbations in the mean square is discussed.Based on the Lyapunov-Krasovskii functional method,by using Chen's integral inequalities,quadratic convex combination and reciprocal convex technique,two novel suffificient conditions are proposed to justify the asymptotic stability of considered impulsive Markovian neural networks in the mean square.The obtained results,which are formed as linear matrix inequalities,can be easily verified via standard Matlab software.Finally,two numerical examples with their simulations are put forward to show the effectiveness of the presented criteria.