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Design Of Robust Controllers For Uncertain T-S Fuzzy Systems

Posted on:2009-03-22Degree:MasterType:Thesis
Country:ChinaCandidate:L QiFull Text:PDF
GTID:2178360308978929Subject:Control theory and control engineering
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The problems of analysis, modeling and control for complex nonlinear systems cannot be well solved by conventional control theories, while fuzzy control may handle these problems efficiently for its full use of expert experiences and language information. T-S fuzzy systems combine the theory of linear system with fuzzy system, they have made great developments in both theory and practice, so they have became a popular topic for analysis and design of complex nonlinear systems.In this thesis, by using Lyapunov stability theory, convex optimization theory and LMI technique, the robust control problems of uncertain T-S systems are studied. How to deal with the interrelations of fuzzy subsystems affects the conservatism of design methods of T-S fuzzy systems. In the past, the interrelations are included in a matrix inequality. In this dissertation, they are expressed as a set of matrix inequalities; so many controller design methods with less conservatism are derived. The main body of this thesis consists of following three parts:The state feedback robust stabilization of T-S fuzzy systems with parameter uncertainties is discussed. The condition is based on quadratic Lyapunov function and it collects the interrelations of fuzzy subsystems into a set of matrixes. Based on the LMI (Linear Matrix Inequality)-based conditions derived, one can easily synthesize controllers for state feedback robust stabilization. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable.The observer-based robust stabilization of T-S fuzzy systems with parameter uncertainties is discussed. First, using Lyapunov stability theory we induced the stability condition of T-S fuzzy control systems, and then get the controller which is described in BMI (Bilinear Matrix Inequality), and can be solved in two steps.The state feedback H∞controller design problem of T-S fuzzy control systems is discussed. For T-S fuzzy systems, an approach of the state feedback H∞controller design with less conservatism is presented and the existence conditions of H∞controller are changed into an LMI problem, which can be solved by convex optimization. Simulations are made for all the theory results in order to verify the validity of the proposed controllers'designs.
Keywords/Search Tags:T-S fuzzy system, robust stabilization, state observer, H_∞control, linear matrix inequality (LMI), bilinear matrix inequalities (BMI)
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