Robust Filtering For Stochastic T-S Fuzzy Affine Systems

In the actual engineering system, various stochastic disturbances are inevitable.When the high performance required, it is necessary to analysis and synthesis thesystem via modeling the stochastic system. Stochastic system usually has the strongnonlinearity, so the traditional control theory is no longer applicable. Also the theo-ry of nonlinear systems has not been formed the perfect framework, there are manyproblems to be solved. In recent years, the T-S fuzzy model has been proved to havegood ability to approximate the complex nonlinear system. Therefore, the complexnonlinear stochastic system model is established combining the general determinedT-S fuzzy model with stochastic system. The structural characteristics of T-S fuzzymodel can make the nonlinear system problems solved by means of the mature theoryof the linear system. On the other part, as the filtering problem is one of the hot issuesin the field of system control and signal processing, huge enthusiasm is devoted to theresearch and fruitful results have been obtained. However, most of the results of therobust filtering for T-S fuzzy stochastic system are based on the common Lyapunovfunctions. This method has great conservative, meanwhile the T-S fuzzy models con-sidered do not involve the nonzero affine term. Based on the existing results, thispaper will give the new results of robust filter design based on piecewise quadraticLyapunov functions for the stochastic T-S fuzzy affine system. The main results areas follows:Firstly, the paper studies the filter design problem of the discrete-time stochasticT-S fuzzy systems with affine term. As the antecedent variables of the system usuallyare the functions of the states, the states may not be all measured, which makes thestates of the system and the states of the filter asynchronous. Based on the piecewisequadratic Lyapunov function and the degenerate elliptic approximating the slab regiondivided, combined with the application of S-Procedure and the decoupling method,the new results of the asynchronous filter design are given. When the system statesare completely measured, the results of filter design of the synchronization are giv-en. Then, the numerical simulation shows the feasibility of the piecewise fuzzy filterdesign.Secondly, by introducing the membership function structure information, theboundary matrices are constructed to guarantee the piecewise quadratic Lyapunov function continuous when across the boundary of the region. Applying the principleof stochastic analysis, Ito differential formula, S-procedure and the Projection Lem-ma, the problem of robust filter design for a class of continuous time It o stochasticsystems based on uncertain T-S fuzzy affine model is studied. The stochastic fuzzysystem considered includes the multidimensional Wiener process, which makes thesystem more general. Firstly the results of synchronous filter design are given whenpiecewise fuzzy stochastic filtering model and the system share the same antecedentvariables. Then, considering the states of the system may not be all measured, new re-search results of asynchronous filter design are further developed. And the numericalsimulation shows the feasibility of the filter design.Finally, through the summary of the whole thesis, the further research contentare put forward.