Stability Analysis Of T-S Fuzzy Control Systems Based On PLIMF And PMIMF

Stability analysis of T-S fuzzy control systems are of very importance in theoryand application of fuzzy control. It is among the vital issues in this feld to make bestuse of information provided by T-S fuzzy control systems to obtain less conservativestability conditions. This paper will take into consideration both the premises and con-sequents of T-S fuzzy control systems to investigate the stability of T-S fuzzy controlsystems. In this paper, we will obtain less conservative stability conditions directlydependent on premises with the help of piecewise linear interpolation to membershipfunctions.First this thesis presents a brief introduction to the history of fuzzy control and theimportance of stability analysis of T-S fuzzy control system. And at the same time, thisthesis summarized the existed results on stability analysis of T-S fuzzy control systemsbriefy.Then the thesis investigates the stability analysis of T-S fuzzy control system withunary membership function with the help of PLIMF. In this part, artifcial T-S fuzzysystems are obtained by PLIMF. With Lyapunov second method, we stabilize the ar-tifcial T-S fuzzy systems and the errors between artifcial T-S fuzzy systems and T-Sfuzzy control systems, resulting in the stabilization of T-S fuzzy control systems andgain the stability conditions in the form of LMI. And then we simplifed the obtainedLMI with the help of”center of gravity” of unary linear functions to make it practi-cal. And the end of this part, the thesis illustrate the reduced conservativeness of theproposed method.With the assistance of PLIMF, this thesis also analyses the stability of T-S fuzzycontrol systems with multivariate membership function. Utilizing the same idea of stability analysis, we acquire the stability conditions in the form of LMI. Again, wesimplifed the LMI through”center of graivty” of multivariate linear functions andillustrate it that the proposed stability conditions in this thesis is less conservative.Finally, this thesis studies the stability issues with PMIMF because it is difcultto fnd the appropriate interpolation regions for multivariate PLIMF while it is rela-tively easy for PMIMF. In this section, we obtain the artifcial T-S fuzzy systems withPMIMF and acquire the stability conditions in the form of LMI through Lyapunovsecond method. Then we simplifed the LMI with”center of gravity” of multilinearfunction and illustrate the decreased conservativeness of the proposed conditions.