Exponential Synchronization Of Discrete Time-delay Neural Networks With Input Saturation Constraints

In the past few decades,the research in many disciplines has involved neural network system,and the research of neural network system has attracted the attention of scholars.On the other hand,in the neural network system,time-delay and saturation are inevitable,and their existence is the main factor that leads to the decline and instability of the system performance.In addition,synchronization has attracted extensive attention because of its clear practical insight in biological systems,social networks and neuroscience.Exponential synchronization of discrete neural network systems with input saturation and time-delay is studied in this paper.By using modified sector conditions,augmented Lyapunov-Krasovskii(L-K)functional and some latest inequalities,sufficient conditions for less conservatism are established.In order to solve the problem conveniently by software,the sufficient conditions obtained in this paper are all expressed by linear matrix inequalities(LMIs).The main research contents of this paper include:1.Aiming at discrete neural network systems with input saturation and time-delay,this chapter studies the corresponding exponential synchronization problem.In order to reduce the conservatism,this paper first designs a memory-based controller with time-delay,and then combines the modified sector condition,the augmented L-K functional,some latest inequalities,and the optimization method to make the allowable initial condition set less conservative,establishes the relevant sufficient conditions in the form of LMIs,and proves that the closed-loop error dynamics are exponentially stable in the local area under this condition.Finally,a numerical example shows that the obtained results are less conservative.2.Under the Round-Robin(RR)protocol,this chapter studies the corresponding exponential synchronization problem for discrete neural network systems with input saturation and time-delay.Firstly,in order to make full use of the limited network bandwidth,when sensors communicate,the order of transmitting information is scheduled by using RR protocol.Then,based on the L-K functional,using the modified sector condition and the latest inequality,in the form of LMIs,the sufficient conditions for the closed-loop system to reach some expected performance indexes are obtained.Finally,a numerical example proves the effectiveness of the obtained results.3.Under the dynamic event-triggered protocol,this chapter considers the corresponding exponential synchronization problem for discrete neural network systems with input saturation and time-delay.Firstly,the dynamic event-triggered protocol is used to schedule the transmission of information.Then,by using the augmented L-K function,combining the delay-dependent sector condition and some latest inequalities,the relevant sufficient conditions are established in the form of LMIs.It is also proved that under this condition,the error dynamics are bounded for the allowable initial conditions.Finally,a simulation example is given to illustrate the effectiveness of the method.