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Relaxed Stability Analysis of Fuzzy-Model-Based Control Systems

Student thesis: Doctoral ThesisDoctor of Philosophy

This thesis presents and extrapolates on the research works concerning the stability analysis of fuzzy-model-based (FMB) control systems. In this study, two types of FMB control systems are considered: 1) Takagi-Sugeno (T-S) FMB control systems; and 2) polynomial fuzzy-model-based (PFMB) control systems. The control scheme illustrated in this thesis has great design flexibility because it allows the number and/or shape of membership functions of fuzzy controllers to be designed independently from the fuzzy models. However, in wake of the imperfectly matched membership functions, the stability conditions of the FMB control systems are typically very conservative given the fact that they are con-gruent with traditional stability analysis methods. In this thesis, based on Lya-punov stability theory, membership-function-dependent (MFD) stability analysis methods are proposed to relax the stability conditions. Firstly, piecewise mem-bership functions (PMFs) are utilised as approximate membership functions to carry out a relaxed stability analysis of T-S FMB control system. Subsequently, PMF-based stability analysis is improved with the consideration of membership function boundary information. Based on the PMF method, we propose a lower-upper-PFM-based stability analysis method. Relaxed stability conditions are obtained in the form of linear matrix inequalities (LMIs) in consideration of the approximation accuracy of the membership function.
For the purpose of stability analysis of PFMB control system, the other MFD method proposed is to extract the regional membership function information via operating domain partition. Two types of membership information are consid-ered in each sub-domain: 1) the numerical relationship between all membership function overlap terms; and 2) the bounds of every single membership function overlap term. Thereafter, relaxed sum of squares (SOS)-based stability conditions are derived. In conjunction with these proposed MFD methods, sub-domain fuzzy controllers are utilised to enhance the capability of feedback compensation. In this thesis, all the LMI/SOS-based stability conditions obtained can be solved nu-merically using existing computational tools. Furthermore, simulation examples are provided to illustrate the validity and applicability of the proposed methods.
Original languageEnglish
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Award date2018

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