Fuzzy Modeling And Controller Design For2-D Discrete Systems

In recent years, as the development of the technology, there has been increasing recog-nition that2-D nonlinear systems have great potential for applications. However, lacking of effective and reasonable model has hindered the progress of2-D nonlinear systems. Motivat-ed by the wide range of application of2-D nonlinear systems, this dissertation carried out a series of fundamental research on fuzzy modeling and control of2-D nonlinear systems. The involved subjects are as follows:1. Taking the spatial and structural features into consideration, a2-D T-S fuzzy model is first established which has a similar configuration of fuzzy modeling as1-D case. The rule structure does not cause an exponential increase of the rule number. When the spatial nature is neglected, then the2-D system reduces to a1-D system. Consequently, the fuzzy modeling configuration is the same as that for1-D fuzzy systems.2. Using the established2-D T-S fuzzy model, the state feedback controller, observer-based controller, output feedback controller are developed to stabilize the closed-loop system. It will be shown that the separation principle holds for the stabilization problem of2-D T-S fuzzy systems. That is, the fuzzy controller and the fuzzy observer can be independently designed, and the resulting closed-loop fuzzy control system, with esti-mated state variables to be used for state feedback control, will be asymptotically stable. Besides, it will be also shown that the separation property is not only sufficient, but also necessary. Hence, no conservativeness will be caused when the fuzzy controller and the fuzzy observer are independently designed.3. The guaranteed cost control problem will be considered for2-D T-S fuzzy systems with norm-bounded parameter uncertainties. The purpose is to design a2-D fuzzy state feed-back controller such that the closed-loop system is asymptotically stable and a specified quadratic cost function has an upper bound for all admissible uncertainties. Sufficient conditions for the solvability of this problem are obtained. By introducing additional free matrices, the existence of guaranteed cost controller increases, and hence the feasible range expands.4. The H∞control problem is considered for the2-D T-S fuzzy model. A2-D bounded real lemma is first established and then a2-D H∞fuzzy controller design is formulated as a convex optimization problem characterized by linear matrix inequalities (LMIs). In designing the H∞controller, the inputs are regarded as variables independent from the states, resulting in only r linear matrix inequalities. The computational advantage is obvious for fuzzy systems with a large number of fuzzy rules.5. A single-step LMI approach to the design of an observer-based H∞controller is pre-sented for the2-D T-S fuzzy model. The single-step approach has successfully avoided the conservativeness of the two-step approach. The separation property in the case of observer-based H∞control framework will be established; that is the fuzzy controller and the fuzzy observer can be independently designed, which guarantee an H∞noise attenuation γ of the whole system (with the fuzzy controller and the fuzzy observer);6. The H∞filtering problem is considered for2-D T-S fuzzy systems. By re-constructing a linear combination of the states, the l2-induced gain from the noise input signal to the estimation error can be guaranteed to be less than a prescribed level, where the noise input is an arbitrary energy-bounded signal. By using basis-dependent Lyapunov functions and the separation technique, sufficient conditions for the solvability of this problem are obtained with less number and less computational demand.