Robust filter design of Takagi-Sugeno fuzzy systems and its applications
Chen Meng · 2008
Industrial processes or systems always exhibit nonlinear or even complex dynamic behavior, which can be in general described or approximated by nonlinear differential or difference equations. In this case, the conventional powerful linear time-invariant control and filtering theory is of little use. Nonlinear system theory is thus developed for analysis and synthesis of a complex nonlinear system if a mathematical model of the system can be established. However, obtaining the solution to a general nonlinear system problem is very difficult if not impossible at all, or the obtained results are too restrictive to be used. Moreover, a global nonlinear model is extremely difficult to build for many complex industrial processes or systems. Quite often no exact mathematical models can be constructed in practice. Thus control and filtering of complex nonlinear systems is still a challenge in the area of systems and control. On the other hand, delays occur in many physical, industrial and engineering systems and are one of the main causes of instability and poor performance of systems. When both complex nonlinearity and time delay are present, the control and filtering of complex nonlinear time-delay systems is even a greater challenge. During the last two decades or so, T-S fuzzy models have been developed to approximate complex nonlinear systems. Unlike conventional modeling which uses a single model to describe the global behavior of a system, T-S fuzzy models are essentially a multi-model approach with simple linear models combined to describe the global behavior of the system, and thus provide alternative approaches to modeling of general complex nonlinear systems. One of the objectives of this thesis is to exploit T-S fuzzy models to construct some systematic H∞ filter schemes for nonlinear systems with time-varying delays. A distinctive feature reported in this thesis is that all the proposed methods are relative to time-varying delays and all filter gains can be obtained by solving a set of linear matrix inequalities. Based on piecewise Lyapunov functions, robust piecewise H∞ filters are proposed