Control And Filter Design Based On Ts Fuzzy Model Of Nonlinear Systems

With the rapid development of science and technology, the research on the control and filtering design of nonlinear delay systems not only have important theoretical significance, but also have important practical value. Based on the T-S fuzzy model, this thesis makes a thorough study for the problem of the control and filter design of nonlinear systems with Linear Matrix Inequality(LMI) and Lyapunov-Krasovskii functional as research tools. The main results are as follows:1. Based on the T-S model, the problem of stability analysis and stabilization for nonlinear fuzzy systems with both state delays and input delays are studied. By constructing a new Lyapunov functional and free-weighting matrices with fuzzy weight method, we give some delay-dependent stability criteria and the stabilization design scheme based on the feasibility solutions of some linear matrix inequalities. Finally, simulation examples show the effectiveness of the results.2. For a class of nolinear continuous delayed system with uncertainties, a new design method of H∞filter is proposed based on the T-S fuzzy model. In the prosedure of design, with fully considering the relation of the terms in equations of systems, we select a new Lyapunov-Krasovskii functional without ignoring some useful terms when estimate the upper bound of the derivative of Lyapunov functional. To some extent, it decrease the conservative. The final conclusion is given by using the linear matrix inequality (LMI) approach. The propoed method guarantees the filtering error system is not only robustly asymptotically stable, but also satisfies H∞performance index under zero initial conditions. 3. The problem of H∞filter design is solved for nonlinear discrete systems with interval time delays. Firstly, a new Lyapunov-Krasovskii functional is also constructed with fully considering the relation of the terms in the equations of systems; secondly, the cross-terms in differential of the Lyapunov-Krasovskii functional are flexible handed by the free-weighting matrices and decoupling technique, and it decreases the conservative induced by the Moon inequalities in other literatures successfully. Simulation results illustrate the effectiveness and the superiority of the method proposed.4. A new method is proposed for the problem of H∞filter design in nonlinear continuous systems with interval time delays. In the prosedure of design, the idea of the delay partitioning is firstly applied in H∞filter design. On the other hand, it also extended to the interval delays for the case of the zero lower bounds of the delays. And it is more suitable for engineering application. Simulation results illustrate the conservatism is further reduced when division increases.