The Study Of Complex Dynamical Networks With Delays And Uncertainties

Uncertain complex dynamical networks are the important network systems. The uncertain systems mainly include two types: dynamic uncertainty and parameter uncertainty. The model's uncertainty is the combination of dynamic uncertainty and parameter uncertainty in general, which may appear on different locations of the control loop. A class of complex dynamical networks with uncertainties, which may be unknown, time-varying but norm-bounded, is studied in this paper. The details are as following:Firstly, the problems of stability for linear complex dynamical networks with either continuous-time or discrete-time uncertainties are studied. Based on the stability theory, by using the method of Lyapunov function, we get some conditions assuring the stability of the complex dynamical networks with uncertainties. These conditions are expressed in the form of linear matrix inequalities, which can be solved easily, and can be applicable to the complex dynamical networks with different topologies. The simulation shows the effectiveness of the proposed approach.Secondly, the synchronization of the complex dynamical networks with delays is addressed. The time delay may appear either in the couple of the network or in the dynamics of each nodes. By using the Lyapunov-Krasovskii functional method, we get the delay-dependent asymptotically stability criteria for networks with delays in terms of LMIs. Based on these conditions, by using the toolbox of LMI, we can get the maximal delay of the dynamical network assuring the asymptotic stability. The results obtained in this thesis can be applied to the dynamical networks with different topologies and sizes.A summary of the full text and the directions for further studies are given at the end of this thesis.