Analysis Of Synchronization And Control For Complex Networks With Switching Parameters

Switched complex network is a class of special complex networks, its node dynamics and topology structure have switching phenomenon. Because the switching often happens in many practical networks, study on switching is very important. As we all know, with respect to many real-world complex networks,due to many internal and external factors, node dynamics are switched systems.On the other hand, link to each node is not always stable in complex networks,link failure and new link creation may happen at times, And then the jumps between different topologies happen occasionally. Today, complex networks with node switching or topology switching have become hot issues. Synchronization for complex networks is that the states of many connected nodes are evolving in synchrony. Today, complex networks with switching phenomenon have been extensively applied in various fields such as robot cooperative control large power supply network. Furthermore, synchronization problem for complex networks with switching has also attracted increasing attention.In the thesis, synchronization and control problems for switched complex networks are studied. Firstly, synchronization for a class of complex networks with all non-synchronized subnetworks by dwell time approach. Secondly, exponential synchronization for a class of delayed impulsive switched complex networks is studied by mean of comparison principle. Thirdly, exponential synchronization for a class of switched neural networks is discussed by average dwell time approach. At last, finite-time synchronization for two cyclic switched complex networks is researched by means of cyclic dwell time approach and finite-time stability theory. The main contents of the thesis are as follows:(1) Global synchronization of switched complex dynamical networks with non-synchronized subnetworks and stochastic disturbances.Based on the dwell time approach and the discretized Lyapunov function technique, the global synchronization problem of switched complex dynamical net-works with stochastic disturbances and all non-synchronized subnetworks is investigated. a sufficient synchronization criterion is obtained in term of linear matrix inequalities and the corresponding switching signal is obtained. The obtained switching signal depends on time rather than the system states, which makes it easier to be implemented. Finally, two examples are provided to illustrate the effectiveness of the theoretical results。(2) Exponential synchronization of hybrid impulsive and switching dynamical networks with delayed impulses. The exponential synchronization problem is investigated for a class of hybrid impulsive and switching dynamical networks. Different from the existing results concerning synchronization of hybrid impulsive and switching dynamical networks, impulsive input delays are considered in our model. Moreover, in our model, the impulsive instances and system switching instances don’t need to be coincident. By using the Razumikhin theorem and the mathematical induction method, several sufficient synchronization criteria are obtained in terms of linear matrix inequalities. The obtained criteria reveal that the frequency of impulsive occurrence, impulsive input delays can heavily affect the synchronization performance. Finally, an example is provided to illustrate the effectiveness of the obtained results.(3) Synchronization of coupled switched neural networks with timevarying delays. The exponential synchronization problem of delayed coupled switched neural networks is investigated by using the matrix decomposing approach、 the switched system comparison principle and average dwell time approach. Here, the topology and node switching are orchestrated by two mutually independent switching signals, respectively. Under the assumption that all subnetworks are self-synchronized and some subnetworks are not self-synchronized respectively, the exponential synchronization criteria are given in terms of algebraic inequalities. Finally, examples are provided to illustrate the effectiveness of the theoretical results.(4) Finite-time synchronization of cyclic switched complex networks under feedback control. Based on feedback control strategy,finite-time synchronization problem is investigated for two cyclic switched complex network-s. By using cyclic dwell time approach and finite-time stability theory, several sufficient criteria have been proposed to ensure the finite-time synchronization for cyclic switched complex networks with or without coupling delays.These sufficient conditions not only supply a method of designing feedback control but also fully reveal the mutual relationship among the cyclic dwell time, the setting time and the initial state. Finally, numerical simulations have been given to illustrated the effectiveness of the proposed results.