Fuzzy Robust Control For Nonlinear Systems

The control problem of nonlinear system has been the research hotspot in the control field and gained various control means. The fuzzy control method has the simplicity of fuzzy controller design and can be applied to a lot of nonlinear systems with better robustness. According to different nonlinear systems, this thesis has modeled the nonlinear system by T-S fuzzy model system, designed fuzzy controller, and discussed the stability definition and stability condition of the system in the frame of Lyapunov stability. Some examples are selected to illustrate the effectiveness of proposed methods. The main contents in this thesis are as follows:1. Firstly, the nonlinear system with uncertainty is modeled by T-S fuzzy model, the concept of the so-called parallel distributed compensation (PDC) is employed to design the state observer and the robust controller which is based on the presented observer. Sufficient condition of the robust controller's existence is presented in terms of linear matrix inequalities (LMIs), and the controller ensures that the fuzzy closed-loop system is quadratic stability with decay rateαand satisfies the given H∞robust performance index.2. Based on T-S fuzzy model, the guaranteed cost control problem of a class of uncertain nonlinear systems with input and state time delay is discussed. By constructing fuzzy state-feedback controller, a sufficient condition that for the given performance index and control law, the closed-loop system is quadratic guaranteed cost stable is presented and expressed in terms of LMIs.3. A class of parametric uncertainties nonlinear time-delay system is modeled by T-S fuzzy system, then the design problem of H∞robust state-feedback controller is addressed, the sufficient conditions that the existence of discussed controller is dependent on the time delay are presented in terms of LMIs, and the resulting closed-loop system also satisfies the H∞robust control performance index. Furthermore, the improved delay-dependent condition of the asymptotic stability for the unforced system is put forward. Numerical examples demonstrate the effectiveness and reduce conservatism of the proposed methods.