H_∞ Filtering For Nonlinear Discrete-time Systems Based On T-S Fuzzy Model

The problem of stability analysis and design for nonlinear systems is an important subject of control theory. Takagi-Sugeno (T-S) fuzzy approach is an effective method of studying nonlinear systems, because it can fully use Lyapunov stability theory to deal with stability analysis and design for nonlinear systems. The problem of filtering for nonlinear systems becomes a very important subject because it is widely applied in many fields such as compositing signal, communication, controlling system. In general conditions, Kalman filtering technique has been applied extensively. When there are uncertainties in dynamic model and the statistics of noise sources are not fully known, the application of Kalman filtering is restricted. H_∞filtering can solve the problem encountered in the applications of Kalman filtering with high accuracy and robustness. Based on the T-S model , this paper deals with H_∞filtering for discrete-time systems. The main contents in this thesis are as follows:(1) Fuzzy H_∞filtering for discrete-time systems with delayed measurement is investigated. By utilizing Lyapunov stability theory and linear matrix inequality method, delay-dependent sufficient conditions which guarantee the stability of the filtering error systems are established. Then, the design approach of such a filter is presented. A numerical example is given to demonstrate the effectiveness of the proposed method.(2) H_∞filtering for discrete time-delay fuzzy systems with missing measurement is discussed. The phenomenon of the missing measurement is assumed to satisfy the Bernoulli random binary distribution and the time-delay is time-invariant. H_∞performance of the filter error system is firstly analyzed by using a basis-dependent Lyapunov functional approach. Then, linear matrix inequality techniques are utilized to design theH_∞filter. An illustrative example is provided to show the effectiveness of the proposed approach.(3) H_∞filtering for discrete time-delay fuzzy systems with probabilistic sensor faults is studied. It is assumed that the probabilistic sensor reductions can be modeled by using a random variable that obeys a specific distribution law. The aim is to design a robustH_∞filter such that the filtering error system is asymptotically mean-square stable with prescribedH_∞noise attenuation level. The design filter is obtained based on the feasible solutions of a set of linear matrix inequalities.