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Researches On Stability Of T-S Fuzzy Control Systems By Considering Information Of Membership Functions

Posted on:2012-10-25Degree:MasterType:Thesis
Country:ChinaCandidate:W C HuFull Text:PDF
GTID:2218330338467201Subject:Power system and its automation
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As an active research field, the fuzzy control theory makes a rapid progress recently. Compared with classical control systems, fuzzy control systems have the following two unmatched advantages. First, it can be easy to realize effectively human control strategies and experience in many applications. Second, it can achieve better control performance in the absence of the mathematic model for the controlled system. Fuzzy logic control is successfully applied to many control problems, such as machine intelligence, signal processing, decision making, pattern recognition, finance, medicine and so on. The Takagi-Sugeno (T-S) fuzzy model which is proposed by Japenese researcher Takagi and Sugeno in 1985 is the most useful model in the fuzzy control theory. This model provides a kind of method for describing complicated nonlinear systems.It is well known that the stsbility analysis is very important in system control and should be considered firstly. Unfortunately, the nonlinear nature of fuzzy control technology sets an obstacle to development of analytic method for stability analysis and of fuzzy control systems. So all the stability conditions we've got until now have some conservativenesses, and how to reduce these conservativenesses arouse people's wide concern progressively. In recent years, a large number of researchers try to improve the stability conditions of fuzzy systems constantly with any method they can imagine, and actually get some good results. Based on these published results, this thesis considered the knowledge of membership functions'shape when developing the stability conditions for T-S fuzzy systems, and gave more relaxed stability conditions. The main research works in the thesis can be described as follows:1. A review of the background, origin and history of fuzzy control systems was firstly presented. Then, the present research situation of stability analysis of T-S fuzzy systems was summarized.2. Briefly introduced the basic knowledge of Lyapunov stability theory and linear matrix inequality (LMI) which will be used in this thesis. Then, expounded the basic model of continuous-time T-S fuzzy systems and discrete-time T-S fuzzy systems. Furthermore, on the basis of the theory of Lyapunov stability, we summarized the stability sufficient conditions when the two models are at the situations of open-loop and closed-loop.3. Considered the knowledge of membership functions'shape when developing the stability conditions for continuous-time T-S fuzzy systems, such as the constraints of product of membership function (overlap level) or the polynomial constraints on shapes of membership functions. After introducing some auxiliary matrix variables, we obtained new LMI-formed stability conditions for the situation of double fuzzy summations, and some numerical examples were provided to illustrate the superiority of these new conditions.4. At the situations of considering the constraints of product of membership function (overlap level) and the polynomial constraints on shapes of membership functions, we provided new stability conditions respectively for double fuzzy summations and multidimensional fuzzy summations. Then, we introdued how to convert the new conditions into LMI's form when used for computing, and some numerical examples were provided to illustrate that the new conditions were less conservative.Finally, some concluding remarks were given, and the future research works were pointed out.
Keywords/Search Tags:Takagi-Sugeno fuzzy systems, Linear matrix inequality (LMI), Stability, Conservativeness, Shape of membership functions, Overlap bounds, polynomial constraints
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