Studies on stability and stabilization of neural networks with time delays

Abstract

The research reported in this thesis deals with the problem of stability and stabilization analysis of certain types of neural networks with time delays. Several sufficient conditions are derived for the stability and stabilization of such systems. More precisely, we study the robust stability and H and#858; control for a class of neural networks and switched neutral-type neural networks with time varying delays and various activation functions. Moreover, the stability and stabilization problems have been analyzed for a class of discrete time stochastic neural networks and stochastic genetic regulatory networks with time varying delays. Next the stability and stabilization results have been investigated for a class of fuzzy neural networks and fuzzy Hopfield neural networks with both discrete and distributed time varying delays. Further we deal with the problem of exponential stability of fuzzy Cogen-Grossberg neural networks with time varying as well constant time delays. Also robust passivity results for stochastic fuzzy bi-directional associative memory neural networks with time varying delays has been discussed. Finally the exponential stability analysis for discrete-time fuzzy stochastic neural networks and discrete-time switched fuzzy neural networks are presented. All the above mentioned results are derived by applying the Lyapunov stability theory, linear matrix inequality technique (LMI) and various analysis techniques like stochastic analysis theory, delay fractioning technique and free weighting matrix approach. The results are established in terms of LMIs which is easily solved by MATLAB-LMI control toolbox. Numerical examples with simulation results are provided in each chapter to illustrate the applicability and efficiency of the obtained results. newline