| Complex networks widely exist in our daily life.Coupled systems,as a special type of complex networks,have attracted considerable attention from many scholars.Numerous scholars are devoted to investigating the synchronization of coupled systems.At present,most of the literature focuses on asymptotic synchronization,which means that the system achieves synchronization on an infinite time interval.However,this type of synchronization may be not optimal since the lifespan of humans and machines is limited,then the concept of finite-time synchronization is put forward.Finite-time synchronization,as the name implies,aims to achieve synchronization in a finite time.Compared with synchronization based on an infinite time interval,finite-time synchronization has excellent disturbance rejection and strong robustness.Therefore,it is very meaningful to study the finite-time synchronization of coupled systems.When studying the dynamical behaviors of coupled systems,control strategy is an effective method to urge systems to realize synchronization.In the real world,the signals are often received through quantization.Therefore,from a practical point of view,this paper uses quantized feedback control to study the finite-time synchronization of two types of coupled systems.On one hand,delay is widespread and ubiquitous,which is one of the most important reasons to induce poor dynamical behaviors of systems.Therefore,considering the impacts of discrete delay and distributed delay on systems meets actual needs.In the second chapter of this paper,the finite-time synchronization of coupled systems with discrete delay and distributed delay is studied.Based on Kirchhoff ’s Matrix Tree Theorem in graph theory and Lyapunov functional method,two synchronization criteria are given to ensure the finite-time synchronization of systems via quantized feedback control.The theoretical results show that,in addition to the coupling strength and control gain,synchronization time has a close relationship with the topological structure of the network.Furthermore,as an application,the theoretical results are applied to coupled oscillators with discrete delay and distributed delay,and the corresponding numerical examples are given to illustrate the validity and feasibility of the theoretical results.On the other hand,the most majority of systems in the real world will be affected by white noise,and the structure or parameters of the system may be subject to some great sudden changes due to some reasons.Therefore,it is meaningful to consider stochastic coupled systems with Markovian switching.In the third chapter of this paper,we study the finite-time synchronization of stochastic coupled systems with Markovian switching.Combining stochastic analysis techniques and M-matrix method with the Kirchhoff ’s Matrix Tree Theorem in graph theory,several sufficient conditions for guaranteeing the finite-time synchronization of systems are given.In addition,an application to stochastic coupled oscillators with Markovian switching is given,and the corresponding numerical simulations which can demonstrate the efficiency and applicability of theoretical results are presented. |
