State Estimation And Simultaneous Analysis Of A Class Of Complex Networks With Mixed Delays

This thesis is concerned with the state estimate and synchronization problem for a class of stochastic complex network with mixed time delays. The complex network under study is involved in both discrete time delay and unbounded distributed time delay, and both time delays are dependent on a Markov chian. i.e., the time delays are mode-dependent In addition, it is also assumed that the nodes of the network are disturbed by a wiener process. First, we cope with the state estimation for the complex network. By constructing the state estimation system and choosing an appropriate state estimation gain matrix, we obtain the desired estimator. Then, by constructing a novel Lyapunov-Krasovskii functional and employing some new analysis techniques, the sufficient conditions are derived to guarantee the mean-square synchronization between the nodes of the network. The obtained criteria, for either the existence of the state estimator or synchronization, can be expressed in the form of inequality (LMI), which can be easily checked by Matlab LMI Toolbox. Finally, two numerical examples are presented to demonstrate the effectiveness and applicability of the proposed methods. It is worth pointing out that our results include the existing ones as the special cases.The thesis falls into three parts. The opening section gives an overview on the related background, and states the significance and the latest progress in the study of the complex networks. We conclude the chapter with the formulation of problems to be investigated in this thesis.In Chapter 2, we begin with introducing the model of the complex network to be studied. A new Lyapunov-Krasovskii functional and some new techniques are employed to deal with the state estimation problem for the given network, the sufficient conditions are derived for the existence of the state estimator, which are in the form of LMI. And a numerical example is used to show our approach.Chapter 3 focuses on the synchronization analysis for the given complex network. Based on Lyapunov theory, and by conducting stochastic analysis, we derive some easy-check criteria for the synchronization between the nodes of the network. An example is given for illustrative purpose. We conclude the chapter with some remarks .