Design Of H_∞ Fuzzy Filter For Nonlinear Time - Delay Systems

As time-delay is frequently encountered in various systems owing to measurement、transmission and computational delays and it is often a source of instability and poor performance. Kalman filter is based on the assumption that the systems are exactly known and their disturbances are Gaussian noises with known statistics. However, when external noise is not precisely known or unavailable, the traditional Kalman filtering is no longer applicable. Therefore, the H∞filtering for systems with time-delay has made this topic of considerable attention. The main advantages of H∞iltering is that it is insensitive to the knowledge of the statistics of the noise signals.This thesis focuses on the problem of fuzzy H∞filter design for nonlinear systems with time-varying delay, a new approach of filter design is proposed by constructing a new Lyapunov function and adopting new free-weighing matrix. Some sufficient conditions for the existence of fuzzy H∞filter is established based on the linear matrix inequality (LMI) approach. Some numerical examples are used to illustrate the effectiveness and the advantage of the proposed method. The main content contains three parts as follows:First, the nonlinear system with time-delay is considered. By means of appropriate Lyapunov functions and free-weighting matrix technique, the problem of fuzzy H∞filter design has been discussed for this kind of system.Then, considering the problem of filter design for nonlinear discrete-time delayed system. Some sufficient conditions for the existence of fuzzy filter are developed in terms of LMIs.Last, since the systems under consideration in the aforementioned two parts do not contain uncertainties, the proposed fuzzy filter design approaches developed in the previous sections are extended to uncertain nonlinear delayed system in this section.