Stability Analysis And Controller Design For 2d Fuzzy Systems

The presentation of two-dimensional(2-D) fuzzy systems models is based onprofound practical background. It appears that 2-D fuzzy system models are muchmore natural, convenient and accurate in representing dynamical systems. It has beendeveloped sufficiently recently, and many classical concepts and results in the standardstate-space theory have been extended to 2-D systems.In this thesis, the problems of stabilization, H_∞control and H_∞filtering are in-vestigated for 2-D fuzzy systems, respectively. The obtained results are formulated interms of the linear matrix inequalities (LMIs). The detailed contents are as follows:(1) The problem of stabilization is addressed for 2-D fuzzy systems. A new cri-terion is given to ensure the system to be stable. Based on this criterion, controllersare designed for 2-D fuzzy systems such that the closed-loop systems have the charac-teristics of asymptotic stability. Finally, the results are shown, via extensive numericalexamples, to be applicable.(2) The problem of H_∞control is discussed for 2-D fuzzy systems. A sufficientcondition is established such that the system is stable and has a prescribed H_∞perfor-mance. Then, the existence conditions of state-feedback and output-feedback controllaws are presented, and thus the closed-loop systems have the above performance.The results obtained are demonstrated to be applicable via numerical examples.(3) The problem of H_∞filtering for is considered by using free-weighting matrixtechnique. A bounded real lemma (BRL) is proposed, which ensures the consideredsystem to be stable with H_∞performance. Based on the BRL, the H_∞filtering problemis solved and the desired filter can be constructed by solving the corresponding LMIs.