The Stability Of Complex Network System With Polytopic Uncertainties

The analysis of stability is one of the most famous problems in the field of complex networks, and receives extensive attention of research scholars all over the world as soon as it was proposed. The analysis of the characteristics of complex networks can not be separated from the analysis of the dynamic system. Because of the diversity and complexity of dynamic system, although there are a lot of relevant conclusions were published, but there are still many problems worthy of study. Uncertainty, as same as time delay, is inevitable in the actual systems, which is one of the important factors that cause the system instability. There are many kinds of uncertainties, and polytopic uncertainty is one of them, which is the focus of this paper. The main contents are as follows:Chapter 1 mainly introduces the significance and the direction of the research on the stability of the complex network. The background and significance of the research on the discrete dynamic systems, the finite time stability and the polytopic uncertainty are emphatically introduced.In the second chapter, the finite-time stability control problem for Markov systems with time-varying polytopic uncertainty is studied. By using Lyapunov stability theory and linear matrix inequality method, the sufficient conditions for the finite-time control of the Markov system with time-varying polytopic uncertainty are given. Numerical simulations verify the validity of the theoretical approach. The problem of finite-time stability is also considered for the system without controller.In the third chapter, a new type of multi-layer switching system is discussed. The three layers of the new model are the switching signal which is influenced by the average dwell time, Markov jump which causes the switch between the subsystems and polytopic uncertainty. Time delay factors are also considered. On this basis, the finite-time stability of the new system is also considered. According to the comparative analysis of the article with other scholars, it is found that many of the research systems in these papers can be considered as special cases of the new multi-layer switching system.In the fourth chapter, the problem of finite-time stability for T-S fuzzy systems with channel fading and uncertainties is studied. Two kinds of uncertainties:norm-bounded uncertainty and polytopic uncertainty are considered in the system respectively to increase the applicability of the results. The channel fading is added in the controller, and the time-delay is also reflected in the system under the concept of channel fading. According to the Lyapunov method and the linear matrix inequality theory, the sufficient conditions are obtained.In chapter 5, the innovation of this paper is summarized; meanwhile, future studies are given.At the end of this dissertation, references are listed.All conclusions are simulated by Matlab to ensure correctness and effectiveness. The simulation results bring into correspondence with the theoretical analysis.