Finite-time Synchronization And Control Of Complex Networks

In this paper,the finite time synchronization of two complex network systems with time-delay complex dynamic network and time-varying time-delay nonlinear coupled neural network under different controllers is discussed respectively.The details are as follows:Firstly,a general controller and an exponential controller are designed for the timedelay complex dynamic network respectively,and two sufficient conditions for achieving finite-time synchronization are obtained by constructing a suitable Lyapunov-Krasovskii function.The synchronization criterion is established based on the integral inequality method and the finite-time control theory,and the estimation strategy of the stability time is given.It is worth mentioning that the results obtained by the above methods do not directly apply the classical finite time stability theory.Therefore,it can be considered that this method is more general.In addition,the exponential controller can shorten the time required to reach the synchronization state compared with the general controller.Next,the finite-time impulsive synchronization problem of nonlinear coupled neural network with time-varying delay is considered.If only stable impulses are considered,it is difficult to synchronize the nonlinear system,so in addition to stable impulses,unstable impulses are also considered.Based on Filippov theory,Lyapunov function method and finite time technique,sufficient conditions for estimating the settling time when the system reaches synchronization under the two control methods are given,and the settling time is not only related to the initial condition but also depends on the impulse sequences,which also makes full use of information of impulse sequences.Moreover,this paper does not use the known average impulsive interval strategy,but analyzes a wider range of impulses in the context of impulse effects.Finally,we mainly explore the cluster synchronization problem of nonlinearly coupled neural networks with time-varying delays.The difference from Chapter 3 is that we divide the nodes set into multiple clusters in this section.Also based on the integral inequality method and finite time stability theory gives the sufficient conditions for achieving cluster synchronization under the two controllers,and gives a strategy for estimating the settling time.