Decentralized Fuzzy Control Of Nonlinear Interconnected Systems With Time-delay Based On T-s Model

As we all know that nonlinear systems exist in the world extensively, so it is important to investigate the stability and control of nonlinear systems. As for nonlinear systems, it is difficult to get the accurate mathematic model. Even we can build mathematic model for those systems, it may be too complicated to design a controller with conventional means. It is the fuzzy control based on knowledge that takes bright future for the above problems.The thesis is concerned with the stabilization problems for the nonlinear interconnected systems with time-delay based on Takagi-Sugeno (T-S) fuzzy model using parallel distributed compensation scheme (PDC), H∞robust decentralized control method in the form of linear matrix inequality (LMI) when the states of the system are available, and not all available, respectively.The main contribution of the thesis may be summarized as follows:(1)Concerning the robust decentralized stabilization problem of a class of the continuous-time nonlinear interconnected systems with multiple time-delay, some sufficient conditions in the form of linear matrix inequality are proposed that guarantee the stability of the system in the sense of Lyapunov asymptotic stability according to Lyapunov stability theory and decentralized control theory of interconnected systems under the circumstances of output feedback. And, systematic observer-based controller design procedures are addressed. Finally, the simulation example is given to illustrate the effectiveness of the proposed methods.(2)Fuzzy decentralized state feedback and observer-based decentralized output feedback controllers are developed for a class of continuous nonlinear interconnected systems with time-delay and the modeling error. First, an equivalent T-S fuzzy model represents the continuous nonlinear interconnected system with time-delay, then fuzzy state feedback controller and observer-based fuzzy output feedback decentralized controllers are designed. The sufficient conditions for the stability of the fuzzy decentralized system with time-delay are proposed by using Lyapunov function combined with linear matrix inequalities. Finally, the simulation example is given to illustrate the effectiveness of the proposed methods.(3) Fuzzy decentralized state feedback and observer-based decentralized output feedback controllers are developed for a class of discrete-time nonlinear interconnected systems with time-delay in the presence of parametric uncertainties.The T-S fuzzy model system with parametric uncertainties is adopted for modeling the nonlinear system, then fuzzy state feedback controller and observer-based fuzzy output feedback decentralized controllers are designed. The sufficient conditions for the stability of the fuzzy decentralized system with time-delay are derived for robust stabilization in the sense of Lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities. The effectiveness of the proposed fuzzy controller and fuzzy observer design methodology is finally demonstrated through numerical simulations.(4)The model reference tracking control problem of a class of the continuous-time nonlinear interconnected systems with time-delay is discussed according to Lyapunov stability theory via H∞robust decentralized control method under the circumstances of state feedback and output feedback. When all the states are available, a state feedback robust decentralized control scheme is developed to override the external disturbances such that the H∞model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, both a decentralized fuzzy observer and an observer-based decentralized fuzzy controller are proposed to solve the H∞model reference tracking control problem for the system.All the sufficient conditions of the control problems are converted in the form of linear matrix inequality. In addition, systematic design procedures are proposed when the states of the system are available, and not all available, respectively.