Synchronization Control And Analysis Of Complex Networks Based On Delayed Impulses

With the rapid development of computer science and engineering technology,more and more scholars pay attention to a complex system which includes nonlinear system control theory,graph theory,biology,physics and mathematics.A large amount of complex data is placed in front of the system,so for the convenience of our research and analysis,we can abstract all the complex dynamic system into a large-scale dynamic system formed by the coupling of multiple nodes according to a certain topological structure.As a special complex network,neural network has become an important research topic in the field of science.Synchronization behavior is not only an important cluster behavior of complex networks,but also an important dynamic characteristic,it exists in all kinds of complex systems.Many scholars have adopted different research methods and techniques.However,among many control methods,impulsive control has attracted more and more scholars' interest due to its security,efficiency,energy saving and other advantages.In network research,delay is inevitable,many reasons may cause the existence of delay,such as signal transmission,sampling,controller design and so on.It is important that in the design of impulsive control,the impulse involving delay can more accurately describe the practical application.Impulse may be beneficial or harmful in real life,so it is necessary to consider the influence of delayed impulse on the performance of complex dynamic system from the point of view of disturbance and control,respectively.Therefore,it is significant and valuable to study the synchronization of complex time-delay neural networks with delayed impulse effect.This paper mainly discusses the synchronization control and analysis of complex neural networks based on delayed impulse effect.The main work of this paper is as follows:In Chapter 1,the research background and significance of complex dynamical networks,synchronization,delay,delayed impulse are introduced,and the influence of delay and delayed impulse on complex dynamical network behavior is pointed out.The main structure of this paper is given.In Chapter 2,we investigate the leader-following synchronization of time-delay neural networks with impulsive control involving delayed impulse.A comparison principle for systems with delayed impulses is proposed,where the effect of time delay in impulses is fully considered.Applying impulsive control theory,some sufficient conditions for synchronization of coupled time-delay neural networks via delayed impulses are derived analytically.Numerical experiments and simulations are given to show the effectiveness of the obtained results.In Chapter 3,we focus on the leader-following synchronization of complex networks subject to delayed impulsive disturbances.The time delays in complex networks contain internal time-varying delays and time-delays involved in impulsive disturbances.By applying the delayed impulsive differential inequality and the linear matrix inequality(LMI),some sufficient criteria that are dependent on time delays are derived in terms of LMI.Meanwhile,a feedback controller is designed to realize desired synchronization via the established LMIs.Note that our developed results relax the requirements of impulse intervals and impulse sizes,and allow the coexistence of delayed impulses and large scale impulses,which are less conservative than the recent works.Finally,numerical experiments and simulations are given to show the effectiveness of the obtained results.In Chapter 4,the stability problem of partial unmeasurable nonlinear systems under impulsive control and the lag synchronization of complex networks with unmeasurable states under impulsive control involving delayed impulse are studied.Some sufficient conditions are given to guarantee exponential stability and lag synchronization of systems using transition matrix method coupled with dimension expansion technique,where the possibility of the effects of partial unmeasurable states is fully considered.In our proposed method,we not only allow systems to have incomplete states,but also relax restrictions on measurable states,which has a wider range of applications in practice.Finally,several illustrative examples are presented,with their numerical experiments and simulations,to demonstrate the effectiveness of main results.