Robust Filtering Design And Fault Detection For T-S Fuzzy Affine Dynamic Systems

Fuzzy logic control (FLC) has attracted great attention during the past decades andit has been shown to be a simple and effective approach to control of many complexnonlinear systems or even nonanalytic systems. On the other hand, filtering and stateestimation has been one of the basic issues in the control theory and engineeringapplication fields. Since Kalman proposed the optimal filter theory in the stochasticsystems, and the Luenberger proposed his observer theory in the certain systems, a lotof research work has been done by the scholars worldwide; On the other hand, the fuzzycontrol technology has been playing an increasingly important role in the realm ofengineering controls since it was proposed. Particularly, the fuzzy theory as well as thefuzzy control technology has been greatly promoted in the industrial process control andreal life with increasingly development of the modern science and the computertechnology.The emphasis in this report is focused on the studies of stabilize analysis androbust filtering design for T-S fuzzy affine dynamic systems based on piecewiseLyapunov functions. The main contents are as follows:Firstly, in this paper we investigated the problem of robust H∞state estimation fora class of continuous-time nonlinear systems via Takagi-Sugeno (T-S) fuzzy affinedynamic models. Attention is focused on the analysis and design of an admissible full-order filter such that the resulting filtering error system is asymptotically stable with aguaranteed H∞disturbance attenuation level. Based on piecewise quadratic Lyapunovfunctions (PQLFs) combined with S-procedure and some matrix inequality linearizationtechniques, some new results are presented for filtering design of the underlingcontinuous-time T-S fuzzy affine systems.Secoondly, we investigated the problem of desining a roubust fault-detectin systemfor a class of discrete time uncertain T-S fuzzy models. The object is to design anadmissible fault dectection filter such that the resulting error system is asympototicallystable with a guaranteed H∞disturbance attenuation level. It is assumed that the plantpremise variable, which are oftern the state variables or their functions, are notmeasurable so that the fault detection filter implementation with statepace partition maynot be synchronized with the state trajectories if the plant. Based on piecewiseLyapunov function and combined with S-procedure and some matrix inequalityconvexification techniques, we derive some new results on filtering design for thediscrete time T-S fuzzy affine system. Finally, a simulation results is provided todemonstrate the effectiveness of the proposed approach. The characters of the approaches in this thesis are as follows: applying the T-Sfuzzy affine dynamic model to approximate the nonlinear systems. It has been shownthat the affine models have much improved function approximation capabilities. Alsothe piecewise Lyapunov functions are much richer classes of Lyapunov functioncandidates than a common Lyapunov function candidate and thus are able to deal with alarge class of fuzzy dynamic systems with less conservative.