The Filter Design For Time-delay T-S Fuzzy Systems

The idea of filer is rooted in the theory of communication, which is a technology to extract useful message from the received signals that contain noise disturbances. The filter-ing problem has attracted extensive attention because it has applications in many industrial environment, such as navigation, target tracking, communication, sound signal processing and so on. From the theory of Wiener filter in 40th of the last century to the robust filter in nowadays, the filtering theory is turning maturity.Fuzzy systems offer an effective method to control the complex systems, bad systems or uncertain systems by using the experts'knowledge. Although the fuzzy theory endures a plenty of arguments, the rushing of the fuzzy productions in industry impulses its develop-ment. The T-S fuzzy model, first proposed by Takagi and Sugeno, is an effect way to describe nonlinear systems, in which a nonlinear system is transformed into a set of linear subsystems. So it provides a good opportunity to employ the well-established theory and tools of linear systems. Therefore, the T-S fuzzy model is powerful to investigate the complex nonlinear systems. The purpose of this thesis is to study several kinds of delayed T-S fuzzy systems and to find conditions for the fuzzy filtering problems on the basis of Lyapunov stability theory. The main results obtained in this thesis are as follows:1. The robust H_{∞}fuzzy filtering problem of uncertain T-S fuzzy neutral systems is studied. Based on the delay-dependent stability condition in the second subsection, a delay-dependent bounded real lemma is obtained. Then, by using the relaxed LMI approach, a sufficient condition of the uncertain T-S fuzzy neutral systems is proposed. At last, two numerical examples are provided to demonstrate the effectiveness of the proposed approach.2. the observer-based filtering problem for the nonlinear T-S neutral delay fuzzy sys-tems is considered. In the industrial producing process, it is impossible that all the states are measurable. And it is available to use outer variables to estimate the state when it unmea-surable. A delay-independent sufficient condition and a delay-dependent sufficient condition are proposed, guaranteeing the stability of the resulting filtering error systems stable.3. Attention goes to the filtering design of robust L₂ - L_{∞}filters for uncertain T-S fuzzy systems with time-varying delay. Based on a common Lyapunov functional and a fuzzy Lyapunov functional, two robust fuzzy filters are designed. By applying the free weighting matrices and the relaxed LMI, less conservatism sufficient conditions are gained. At last, two numerical examples are given to prove the correctness of our method.4. The problem of delay-dependent non-fragile robust H_{∞}filtering for uncertain time- varying T-S fuzzy delay systems is addressed. Attention is focused on the design of a filter when its parameters change it can keep the filter error systems stable and satisfy the H_{∞}per-formance. The approached of free weighting matrixes and relaxed LMI are used to further reduce the conservatism. The numerical examples are provided to demonstrate the effective-ness of the design method.5. A time-varying industrial model is used to demonstrate the effectiveness of the proposed filters in the work before. Investigating a continuous stirred tank reactor(CSTR) model, we emulate the non-fragile robust H_{∞}fuzzy filter, the robust L2 - L_{∞}fuzzy filter un-der a normal Lyapunov function and the robust L2 - L_{∞}fuzzy filter under fuzzy-weighting Lyapunov function, and get good results.6. We conclude the thesis and point out some open problems that should be further studied.