A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

摘要

This paper reviews the stability analysis of continuous-time fuzzy-model-based (FMB) control systems, with emphasis on state-feedback control techniques, which is an essential issue received a great deal of attention in the fuzzy control community. It gives an overview of the milestones and the trend of developments and achievements for the past decades. Focusing on the stability analysis of FMB control systems, it summarizes the issues in the four fundamental and essential aspects, namely, the types of membership-function matching, types of Lyapunov functions, types of stability analysis and the techniques of stability analysis are discussed. To start with systematic discussion, the FMB control systems are categorized into three types of membership-function matching, namely, perfectly, partially and imperfectly matched premises, regarding the premise membership functions and the number of rules used in the fuzzy model and fuzzy controller which forms the FMB control system. The features of each category are thoroughly discussed from theoretical to practical point of view. Various types of Lyapunov functions available in the literature for conducting stability analysis and their characteristics are then reviewed. Especially, the focus of this paper is to promote the concept of membership-function-dependent (MFD) stability analysis, which makes use of the information of membership functions aiming to relax the stability conditions compared with the dominant membership-function-independent (MFI) stability analysis in the literature. The techniques for MFI and MFD stability analysis are then discussed in details, which provide some solid ideas to analyze the stability of FMB control systems. More importantly, it sheds light on the fact that MFD stability analysis demonstrates a greater potential than the MFI one for relaxing the conservativeness of stability analysis results, which points a promising research direction for this topic. The purposes of this paper are to provide a comprehensive update for the stability analysis of FMB control systems to the researchers in the field and serve as a quick guide for the potential researchers who want to enter the field.