Global stability analysis of delayed neural networks with impulses

Abstract

The neural networks have been extensively studied because of its successful applications in many areas such as image processing, pattern recognition, newlineassociative memory, signal processing, optimization solvers and so on. Some newlineof these applications highly depends on the stability of the equilibrium point of newlineneural networks. Consequently, the stability analysis is essential for the design newlineand execution of neural networks and hence the stability analysis problem for newlineneural networks has attracted considerable attention in recent years. In hardware implementation of neural networks, time delays are unavoidably encountered due to the finite speed of the switching and transmission of signals in a newlinenetwork. Further, when performing the computation, there are many stochastic newlinedisturbances that affects the stability of neural networks. While in practical operation, the stochastic interruption often appears in the electrical circuit design newlineof neural networks. The stochastic disruption is also capable of causing a destabilization in the neural system. Moreover, Markovian jump system can be used newlineto model abrupt cases such as random failures, changes in the interconnections newlineof sub systems and sudden environment changes, etc. newlineOn the other hand, many physical systems undergo abrupt changes at certain moments of instantaneous perturbations, which leads to impulsive effects. newlineNeural networks are frequently subjected to impulsive perturbations which in newlineturn affects the dynamic features of neural networks. Neural networks can be newlinefurther classified into two categories, such as the continuous-time and discretetime. In recent years, there have been many notable works on the continuoustime neural networks. Similarly, the discrete-time neural networks in operation, newlineis more applicable to problems that are inherently temporal in nature or related newlineto biological realities and it can ideally keep the dynamic characteristics, functional similarity and even the physical or biological reality of the continuoustime networks under mild restriction.