Quantized H_∞ Filtering For T-S Fuzzy Systems

With the development of the science and technology, digitization and network have gradually become the mainstream of the control systems. This is because that, compared with classical control theory, the quantized effect is not considered, while in actual control systems, quantization is unavoidable, which usually degrade the controller/filter performance or cause system instability by using traditional control theory. In order to study the quantized problem, widely studied has been by researchers at home and abroad, many significant results have been proposed. On the other hand, classical control theory is based on mathematical model, control systems investigated becomes more and more complex, so it is hard to establish its mathematical model with satisfied precisions. For this case, the conventional control theory is not applicable. With the purpose of resolving this problem, the fuzzy control techniques with a property of human language can overcome the difficulties has been invented. In particular, as effective tool for deal with nonlinear systems, the controller/filter design and stability analysis based Takagi-Sugeno(T-S) model for nonlinear systems have appealed researcher’s interest and many important achievements have been obtained.This thesis makes a thorough study for the problem of H?filtering(state estimation) of T-S fuzzy systems with quantized measurements. LMI(Linear Matrix Inequality) method has been proposed to design a H?filter, which ensured not only the asymptotical stability but also a prescribed H?performance under the premise that the quantized error effect can be mitigated. Generally speaking, our specific idea is that consider the system output is quantized by a static time-invariant logarithmic quantizer quantization, by using the existing conclusions the quantized problem is equivalent to the traditional robust problem by treating the quantization error as a norm of bounded uncertainty. Then, the filtering error system is given by taking the H?performance considered. Furthermore, we can obtain the filter design conditions based on Lyapunov functional method which separates the Lyapunov matrixes from systems matrixes by using effective matrix transformation techniques and Lemmas. Simultaneously, a numerical simulation of tunnel diode circuit is given to demonstrate the effectiveness of the proposed approaches.At last, the work in this paper is summarized and further research topics arepointed out.