Global Stability Analysis for Fuzzy Systems and Tracking Control

• Main Authors: Cheng-Wei Lu, 呂政緯
• Other Authors: Kuang-Yow Lian
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/4q3xfm

碩士 === 中原大學 === 電機工程研究所 === 91 === Recently, there has been a rapid growing interesting in using T-S fuzzy model to approximate nonlinear system. The T-S fuzzy model which originates from Takagi and Sugeno mainly deals with the nonlinear systems. With using this model, the nonlinear system is represented by several fuzzy subsystems in fuzzy IF-THEN rules where the con-sequent part is linear dynamical equation. Blending these IF-THEN rules, we can exactly represent the original nonlinear system. When consider the controller and observer design, we use the conception of parallel distributed compensation (PDC) to carry out these designs. We discuss the stability analysis of T-S fuzzy systems by using the Lyapunov's direct method. The sufficient conditions are formulated into linear matrix inequalities (LMIs). Typically, the stability analysis is investigated in local region due to the local sector nonlinearity. We introduce the concept of region of model and region of stability to characterize the stability property. The stability region can be obtained by using the level set of Lyapunov function. In addition, a global stability condition is addressed. As a second part of thesis, we discuss the tracking control of nonlinear systems by using T-S fuzzy model. To cope with the problem of immeasurable states, the observer-based fuzzy controller is our main concern. An H 1 performance criterion is proposed to attenuate the disturbance due to immeasurable premise variables. Furthermore, an asymptotical tracking can be achieved when the disturbance is with a Lischitz-type property. All the stability conditions and the derivation of control gains are converted into LMIs problems which can be solving by Matlab’s toolbox.