Stability Analysis Of Complex Dynamic Network System Based On T-S Fuzzy Model

The study of Complexity and Complex networks has been a focus subject of today the scienti?c community. Complex networks are presently signi?cant tools and methods to describe and understand the complex system, which highly summarize the complex system as the networks consisting of many interacting individuals or nodes. Complex networks have been used widely in di?erent scienti?c ?elds, such as biological sciences, sociology, engineering, physics, computer science and so on, which have become a brilliant research topic of complexity science ?eld. Stability is widespread in the various kinds of complicated network systems, and consensus is a typical collective behavior in complex networks and one of the most important dynamic characteristics of complex networks as well.Actually the practical networks are mostly non-linear systems, and the traditional automatic controller integrated design should be based on accurate mathematical model of controlled object. While fuzzy control do not need to know the process of accurate mathematical models. Fuzzy control is with anti-interference ability,fast response, and strong robustness for the system parameters changing. The T-S fuzzy model can be in?nite approximation of nonlinear system, and by using parallel distributed compensation algorithm the analysis and controller design for the nonlinear network systems can be turned into the study of linear problems.When the system is disturbed and the presence of uncertainties, the stability of the system tend to be very seriously a?ected, and sometimes tend to be unstable. Therefore, the stability and consistency of fuzzy nonlinear networked control systems are with theoretical and practical value.Based on the T-S fuzzy model, the analysis and controller design are considered for the nonlinear network systems. The main work of this study are as follows:(1)State output feedback control based on the T-S fuzzy model complex dynamic network system:For a class of discrete-time nonlinear complex dynamical network systems based on T-S fuzzy model, investigates the stability and the consensus of the systems. The nonlinear complex dynamical network system consists of N discretetime T-S fuzzy subsystems, and parallel distributed compensation algorithm and Lyapunov method are used to analyze the stability of system. Furthermore, the consensus problem for the leader-follower complex dynamical network is considered. And the proposed criterion can be obtained by solving a set of linear matrix inequalities(LMIs) which are numerically feasible.(2)State output feedback and static output feedback control based on T-S fuzzy model uncertainty complex dynamical systems:For a class of T-S fuzzy models with parametric uncertainty nonlinear interconnected systems, considering the role of disturbances, the analysis of the stability and H∞performance of the system are considered, then the state output feedback controller and the static output feedback controller is designed. A decentralized state feedback fuzzy control scheme is developed by the parallel distributed compensation algorithm. The stability analysis for the nonlinear interconnected systems is given. Furthermore, consensus analysis for the leader-follower interconnected systems is obtained, the consistency problem can be converted to the stability of the error system, and for the consistency the state output feedback controller and the static output feedback controller is designed. All these results are characterized in terms of linear matrix inequalities(LMIs), which can be solved ef-?ciently in practice by convex programming technique. Finally, simulation results show the e?ectiveness of the proposed methods.