Stability Analysis And Control Synthesis For 2-D Discrete Stochastic T-S Fuzzy Systems

As the widely used of 2-D discrete stochastic nonlinear systems, it has attracted more and more attention of investigators. Owing to the complexity of 2-D nonlinear systems, the establishment of the systemic and effective model of 2-D nonlinear systems have become an urgent problem. Therefore,2-D discrete stochastic T-S fuzzy model and 2-D discrete stochastic T-S fuzzy polynomial model have been proposed in this dissertation to carried out a series of research on 2-D discrete stochastic nonlinear systems. The involved subjects are as follows:1.2-D discrete stochastic T-S fuzzy model is established. Then, stability analysis and the design of H∞ fuzzy controller are investigated. An H∞ fuzzy controller is designed via solving a convex optimization problem characterized by linear matrix inequalities (LMIs) to stabilize the closed-loop system. Based on the variable separation technology, a sufficient condition for the existing of H∞ fuzzy controller, which contains only r LMIs, is gained. And then corresponding state feedback controller is designed. Two examples are given to illustrate the effectiveness of the proposed approach and less conservation of the second approach.2. H∞ FD problem is considered for 2-D discrete stochastic T-S fuzzy model. The purpose is to design a fuzzy FD filter such that the FD system is mean-square asymptotically stable and has an H∞ noise attenuation γ. By considering the output and system input information as independent variables, system is re-constructed. A new sufficient condition for the existence of FD filter with less LMI constraints is derived, and the FD filter is re-designed. Then, it has been shown that the two conditions are equivalent. Hence, no conservativeness is caused. An example is given to demonstrate that the FD filter can detect the fault efficiently, and the FD existence condition based on the re-construct system is available on wider feasible domain than the other one.3. The H∞ control problem of state-delay 2-D discrete stochastic T-S fuzzy model is investigated. By employing an appropriate state-delay dependent Lyapunov-Krasovskii functional and introducing additional freedom matrices, the state-delay dependent sufficient conditions for the stability of state-delay 2-D discrete stochastic T-S fuzzy model and the existing of H∞ fuzzy controller are obtained, and the H∞ fuzzy controller is designed. By using the separation technique, the number of the conditions for stabilization is reduced. An example is provided to demonstrate the effectiveness of the approach.4.2-D discrete stochastic T-S fuzzy polynomial FMII model is established, it takes the models proposed in Chaper 2 as special cases. Sufficient conditions for the mean-square asymptotically stable of the proposed model is obtained by solving a convex optimization problem characterized by SOS constraints, and the corresponding H∞ fuzzy polynomial controller is designed. Moreover, H∞ control problem of 2-D stochastic T-S fuzzy polynomial Roesser model is investigated. The H∞ fuzzy polynomial controller is designed. Examples are proposed to illustrate the effectiveness of the approaches.