| Summary: | 碩士 === 中原大學 === 電機工程研究所 === 90 ===
Nowadays, T-S fuzzy model is a rapid growing modeling method which
originates from Takagi and Sugeno. It is described by fuzzy IF-THEN rules
where the consequent parts are local linear models. So it can easily
approximate or exact represent a nonlinear system. Once a fuzzy
representation of a nonlinear system is described by if-then rules, the
control problem becomes to find a local linear or nonlinear compensator to
achieve the desired objective. When considering controller and observer
design we use the conception of parallel distributed compensation (PDC) to
carry out these designs. The stability analysis and controller synthesis are
then systematically formulated into linear matrix inequalities (LMIs). The
LMI problem can be solved very efficiently by convex optimization techniques.
In this thesis, we will first study the relaxed stability conditions of a
nonlinear system. By using the relaxed stability conditions we can get the
numerical solution more easier. Furthermore, we know that measuring full
states can be difficult and costly because sensors are often subject to
noise. An observer is designed to estimate the immeasurable states. Notice
that the premise variables in the fuzzy observer are assumed to be
measurable in general. However, this assumption of measurable premise
variables imposes a strict constraint on the applicability of this design in
practical situations. Therefore, we shall give some discussion about the
premise variables of the fuzzy observer depend on the estimated state
variables. Finally, we discussed the stability of T-S fuzzy model via fuzzy
Lyapunov function. It has been paid a lot of attention in recent years due
to avoiding conservatism of stability and stabilization problems. Fuzzy
Lyapunov function sometimes be called multiple Lyapunov function and it
shares the same membership function of plant which is in Takagi-Sugeno fuzzy
model. A relaxed condition derived here is represented in terms of LMI and
then Matlab's toolbox can be used to get the control gains.
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