Stability analysis of fuzzy-model-based control systems: Linear-matrix-inequality approach

Inspired by the fuzzy set theory established by Zadeh in 1965, Mamdani proposed fuzzy controllers to tackle nonlinear systems [86, 87]. Since then, fuzzy control has become a promising research platform. Despite the lack of a concrete theoretical basis, many successful applications of fuzzy control were reported in various areas such as sludge wastewater treatment [115], control of cement kiln [39], etc. These successes show that fuzzy controllers are capable of handling ill-defined plants with significant parameter uncertainties. As pointed out by Mamdani, stability of fuzzy systems is an important issue, and the remarked disadvantage of fuzzy control is the lack of appropriate tools for the analysis of controller performance [47]. In the absence of an in-depth analysis, fuzzy control systems may come with no guarantees of stability, good robustness and satisfactory performance; even some guidelines or rules-of- thumb for designing fuzzy controllers may not be available. In view of these limitations, a lot of research work had been done during the past two decades.