Robust Stability Analysis And H_∞ Control Of T-S Fuzzy Systems With Real Parametric Uncertainty

The research of fuzzy control theory includes a series of main aspects, such as the stability and robustness analysis, the system design approach and the improvement of system performance etc. The research of T-S fuzzy control systems has become one of future explorations of nonlinear uncertain systems.Based on the theories of Lyapunov stability, the paper deals with the problems of robust stability, quadratic stability and H∞control of a class of T-S fuzzy systems with real parametric uncertainty in terms of linear matrix inequalities (LMIs). Then new conditions for robust stability of the T-S fuzzy systems are given. And we also study the conditions for H∞control problem, and give the design methods of the state feedback H∞controller. Numerical examples are presented to illustrate the effectiveness of the method, providing helpful reference to further analysis and research of the T-S fuzzy systems.The contents are as follows:Chapter one is the general introduction to T-S fuzzy systems, including its development, stability, H∞control research, the basic structure of logic fuzzy systems. Relative linear matrix inequalities (LMIs) are also introduced in this part.Chapter two is on the robust stability of T-S fuzzy systems. Firstly, the stability of the T-S fuzzy systems is briefly stated, then gives the description of the system to study and the robust stability, coming to a new condition of the robust stability by using the linear matrix inequalities (LMIs).Aiming at the uncertain T-S fuzzy systems, Chapter three discusses the quadratic stability, which refers to the quadratic stability of colse loop system coming from the state feedback, and arrives at two necessary conditions for quadratic stability and laies a theoretic foundation for the H∞control study.Chapter four is mainly on H∞control of T-S fuzzy systems with real parametric uncertainty. Focusing on design methods of the state feedback H∞controller, the chapter describes the system model and H∞control problem first, and tells the design method of the state feedback H∞controller based on linear matrix inequalities (LMIs), and proves the effectiveness of the method and offers numerical examples at last.The last chapter summarizes the research study, and suggests the subsequent research direction.