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

The problem of stability analysis and design for nonlinear systems isan important subject of control theory. Takagi-Sugeno (T-S) fuzzyapproach is an effective method of studying nonlinear systems, because itcan fully use Lyapunov stability theory to deal with stability analysis anddesign for nonlinear systems. The problem of filtering for nonlinearsystems becomes a very important subject because it is widely applied inmany fields such as compositing signal, communication, controllingsystem. In general conditions, Kalman filtering technique has beenapplied extensively. When there are uncertainties in dynamic model andthe statistics of noise sources are not fully known, the application ofKalman filtering is restricted. H_∞filtering can solve the problemencountered in the applications of Kalman filtering with high accuracyand robustness. Based on the T-S model, this paper deals with H_∞filteringfor discrete-time systems. The main contents in this thesis are as follows:(1) Fuzzy H_∞filtering for discrete-time systems with delayed measurementis investigated. By utilizing Lyapunov stability theory and linearmatrix inequality method, delay-dependent sufficient conditions whichguarantee the stability of the filtering error systems are established.Then, the design approach of such a filter is presented. A numericalexample is given to demonstrate the effectiveness of the proposedmethod.(2) H_∞filtering for discrete time-delay fuzzy systems with missingmeasurement is discussed. The phenomenon of the missingmeasurement is assumed to satisfy the Bernoulli random binarydistribution and the time-delay is time-invariant. H_∞performance ofthe filter error system is firstly analyzed by using a basis-dependent Lyapunov functional approach. Then, linear matrix inequalitytechniques are utilized to design the H_∞filter. An illustrative exampleis provided to show the effectiveness of the proposed approach.(3) H_∞filtering for discrete time-delay fuzzy systems with probabilisticsensor faults is studied. It is assumed that the probabilistic sensorreductions can be modeled by using a random variable that obeys aspecific distribution law. The aim is to design a robust H_∞filter suchthat the filtering error system is asymptotically mean-square stablewith prescribed H_∞noise attenuation level. The design filter is obtainedbased on the feasible solutions of a set of linear matrix inequalities.