Fuzzy Control Of Nonlinear Systems Based On T-S Model

Compared with classical control systems, fuzzy control systems have the following two unmatched advantages. First, it can be easy to realize effectively human control strategies and experience in many applications. Second, it can achieve better control performance in the absence of the accurate mathematic model for the controlled system. In 1985, Takagi T and Sugeno M proposed the Takagi-Sugeno (T-S) fuzzy model, which brings far-researching impact on fuzzy control theory and its application, and makes the stability analysis of fuzzy systems to a new theoretical height. Combining with the Lyapunov stability theory, robust control theory and H∞control theory, using the Linear Matrix Inequality (LMI), this thesis discussed the stability and stabilization problems of fuzzy systems based on T-S linear model and T-S bilinear model in detail, respectively.The main research works in this thesis can be described as follows:1. By constructing new appropriate fuzzy Lyapunov function and considering the useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov function, the delay-dependent stability criteria of open-loop fuzzy systems with time-varying delay are derived. Then, based on parallel distributed compensation (PDC) scheme, the delay-dependent stabilization conditions of the closed-loop systems are derived and the corresponding state feedback controller can be obtained, respectively.2. Based on fuzzy Lyapunov function and fuzzy free-weighting matrices with time-varying delay, some new sufficient conditions for robust H∞stabilization of uncertain continuous-time fuzzy system with time-varying delay are given. The fuzzy free-weighting matrices are introduced, the purpose of which is to relax the constraint of the derivatives of time-delay.3. In order to reduce the conservation of the common Lyapunov function,based on fuzzy Lyapunov function and PDC scheme, the H∞stability analysis of fuzzy delay discrete-time systems and robust H∞stability analysis of uncertain fuzzy delay discrete-time systems are studied, respectively. Introducing the relax matrix, the fuzzy controllers design is presented in the form of LMIs, respectively.4. Stability analysis and synthesis of continuous-time nonlinear systems based on the T-S bilinear model are investigated. By using Lyapunov function and PDC scheme, some sufficient conditions for multiple inputs fuzzy bilinear systems to be robust H∞stable are derived. Then, the delay-dependent stability of fuzzy systems with time-varying delay both in state and input is discussed and an LMI based controller design method is obtained. Finally, based on the static output-feedback controller, some sufficient conditions for the fuzzy bilinear systems to be stable are obtained in the form of LMIs.5. The stability of discrete-time fuzzy bilinear systems based on the T-S bilinear model is analyzed. By using Lyapunov function, some sufficient conditions for multiple inputs discrete-time fuzzy systems to be stable are derived. Then, the problem of stability analysis and synthesis of fuzzy systems with time-delay both in state and input are discussed. Sufficient conditions are derived for stabilization and are formulated in the form of LMIs. Finally, based on the piecewise Lyapunov function and switching fuzzy model, considered the interactions among the fuzzy subsystems in each subregion, the relaxed stabilization conditions are obtained for the fuzzy bilinear systems.6. In the presence of the additive controller gain perturbations, the non-fragile guaranteed cost control problems for the continuous-time and discrete-time fuzzy bilinear systems with time-delay in both state and input are considered, respectively. Based on the PDC approach, the non-fragile guaranteed cost state feedback controllers design is obtained, such that the closed-loop systems are asymptotically stable and the closed-loop performance is no more than a certain upper bound of a given quadratic cost function.7. The problem of decentralized robust control for a nonlinear interconnected system composed by T-S bilinear models with interconnections is considered. Based on the Lyapunov stability analysis theory and decentralized control theory, some sufficient robust stabilization conditions are derived for the whole closed-loop fuzzy interconnected systems.Finally,some concluding remarks are given, and the future research works are pointed out.