Asymptotic Behavior Analysis Of Two Kinds Of Inertial Neural Networks

Asymptotic behavior analysis of real-valued inertial neural network and complexvalued inertial neural network are investigated based on Lyapunov-Krasovskii functionals,inequality techniques and the properties of nonnegative matrix.The quasi-invariant sets,attractive sets,exponential synchronization,exponential convergence and exponential stabilization are mainly studied.This paper is consisted of six chapters with the structure listed as follows:In Chapter 1,we introduce the research status of real-valued neural network,impulsive complex-valued neural network,state estimation and invariant set of neural network,inertial neural network.In Chapter 2,the quasi-invariant and attractive sets for inertial neural networks with time-varying and infinite distributed delays are studied.By utilizing the properties of nonnegative matrix,a new bidirectional-like delay integral inequality is developed.Some sufficient conditions are obtained for the existence of the quasi-invariant and attractive sets of system.Besides,the framework of the quasi-invariant and attractive sets for the system is provided.In Chapter 3,the problem on the exponential convergence of impulsive complex-valued inertial neural networks with time-varying delays are discussed.By constructing Lyapunov-Krasovskii functionals,some delay-dependent sufficient conditions about linear matrix inequality are proposed to ascertain the global exponential convergence of the addressed neural networks with two classes of complex-valued activation functions.In Chapter 4,exponential synchronization for inertial neural networks with mixed time-varying delays by virtue of intermittent control schemes is concerned.By constructing Lyapunov-Krasovskii functionals and employing inequality techniques,several useful exponential synchronization criteria are obtained.In Chapter 5,the problem on the exponential stabilization of complex-valued inertial neural networks with time-varying delays via impulsive control is investigated.Based on matrix measure and applying impulsive differential inequality,some easily verifiable algebraic criteria on delay-dependent conditions are derived to ensure the global exponential stabilization for the addressed neural networks using impulsive control.And the exponential convergence rate index is also estimated.In Chapter 6,we will summarize the full text and point out the developing directions that needs to be further explored in the future.