Dissertation > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Cybernetics ( control theory, mathematical theory )

Stability Analysis of a Class of T-S Fuzzy Control System

Author LiuJun
Tutor JinChaoYong
School Guangdong University of Technology
Course Applied Mathematics
Keywords Fuzzy Control System T - S fuzzy systems Stability Analysis Common quadratic Lyapunov function Fuzzy differentiation Piecewise quadratic lyapunov function Linear matrix inequality (LMI)
CLC O231
Type Master's thesis
Year 2011
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Fuzzy control is based on the theory of fuzzy mathematics, language rules and fuzzy reasoning advanced control strategies, it is an important branch of the modern theory of intelligent control its rapid development and wide application, effectiveness significantly interesting. compared to conventional control, fuzzy control has the incomparable advantage of the huge, fuzzy control is mainly used as a non-linear function approximation tools Takagi and Sugeno 1985 TS fuzzy model bring to the study and application of fuzzy control theory a far-reaching impact of the fuzzy system stability analysis risen to a new level of theory, and many results have been applied to the actual object TS fuzzy model advantage of it to make full use of the Lyapunov stability theory to systems analysis and controller design, fuzzy modeling of nonlinear systems TS, and then provide a systematic method to study the nonlinear stability of the system as well as the controller design problem. stability analysis and design methods of fuzzy control systems fuzzy theory an important research topic, but the essence of the fuzzy control system is non-linear, and therefore the stability analysis more difficult. far, although there are many kinds of fuzzy system stability theory, but have not yet formed a complete theoretical system, there are many theoretical issues to be further in-depth research paper aims to system stability of TS fuzzy system, in-depth study of some innovations in the theoretical aspects, provides a new idea for the stability of TS fuzzy system, the new method The first chapter describes the background and development of the fuzzy control theory, a brief analysis of the basic idea of ??fuzzy control theory, simple overview of the development of the domestic and international fuzzy control theory research and progress and technology second chapter the basic theory and the concept of the fuzzy control system, also introduced fuzzy control system stability analysis method we have a general understanding of the fuzzy control system. these basics of this research work provides certain theoretical basis of Chapter III system controlled object TS fuzzy modeling, charged for TS fuzzy model stability discriminant problem. article discussed continuous TS fuzzy model and discrete TS fuzzy model both cases, and on this basis, given the form of a theorem TS model, the open-loop system and the closed-loop system stability condition Chapter Feng, Johnsson, Ren et al piecewise Lyapunov function foundation, study the nature of the input fuzzy control system using double overlapping fuzzy differentiation, the sufficient conditions for a wider range of stability judgment given on the basis of the conditions to avoid the common quadratic Lyapunov function conservative strict restrictions, and need not be given membership function and last through concrete examples to verify the effectiveness of the method.

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