A Review on Interval Type-2 Fuzzy-Model-Based Control Systems: Membership-Function-Dependent Perspectives

The (type-1) fuzzy-model-based (FMB) control design offers a viable solution to address nonlinear control challenges in a systematic way. Recently, interval type-2 (IT2) FMB control has drawn attention from researchers due to its superior capability of handling uncertainty, which inevitably appears in real-world systems. This review article gives an overview of the development of stability analysis of continuous-time IT2 (Takagi–Sugeno and polynomial) FMB control systems delivered in the following topics: overview, IT2 fuzzy models, IT2 fuzzy controllers, stability analysis of IT2 FMB control systems, as well as potential research topics. This review will start by giving an overview of type-1/type-2 model-free and type-1 FMB control methods and their shortcomings that can be overcome by using the IT2 FMB control design. We will identify the difficulties in analyzing the stability in terms of modeling concerns, controller issues, and analysis tools. In terms of fuzzy modeling, we will recall the preliminary concept and techniques for the IT2 polynomial fuzzy model. In terms of fuzzy controlling, we define the IT2 state-feedback polynomial fuzzy controller. In addition, from an implementation perspective, an IT2 fuzzy controller must be well defined, i.e., uncertainty-free, which reduces it to a type-1 fuzzy controller. Then, a summary of stability analysis techniques and results will be discussed. This article explores the role of the imperfect premise matching (IPM) concept and membership-function-dependent (MFD) analysis techniques in contributing to the stability analysis. We will then discuss some potential topics related to IT2 FMB control systems. This review article summarizes the recent development and findings of stability analysis of continuous-time IT2 FMB control systems, contributions, perspectives, concepts, and ideas from the authors. It serves the purposes of offering a comprehensive overview of the topic; developing insight into the topic by justifying the need for IT2 FMB control and underpinning concepts; shedding light on stability analysis realized by the IPM concept and MFD analysis techniques; and promoting the research by proposing variants of models and controllers and potential research directions.