T-S Model-Based Robust Non-fragile Fuzzy Control Of Nonlinear Systems

With development of science, technology and productivity, the plantsto be controlled are becoming more and more complex. For lack ofaccurate mathematical model, existing of various nonlinear sections anduncertainties in practical systems, it is important and significant toinvestigate the stability synthesis and control problem of nonlinear systems.However, there is no efficient method to solve this class of problems. Aswe know T-S fuzzy models can approximate nonlinear system significantly,and it is easy for us to analyze. T-S model-based fuzzy control method hasbeen the hotspots in the investigation of nonlinear systems. In this paper,the guaranteed cost control and non-fragile control problems of nonlinearsystems have been investigated based on T-S fuzzy models.First, for a class of T-S fuzzy systems with norm-bounded parameteruncertainties, the problem of designing an optimal guaranteed cost fuzzycontroller is considered via the PDC (parallel-distributed compensation)approach applied with linear matrix inequalities (LMIs). So that theclosed-loop performance is no more than a certain upper bound in thepresence of the norm-bounded parameter uncertainties. Second, the non-fragile guaranteed cost control problem for a class ofnonlinear systems described by T-S fuzzy model is concerned. Theobjective is to design a state feedback controller such that the closed-loopperformance is no more than a certain upper bound in the presence of theadditive controller gain perturbations. A condition for the existence ofnon-fragile guaranteed cost controllers is derived via the linear matrixinequality (LMI) approach.In the end, we take the uncertainties of plant and controller intoconsideration in the same problem. By combining the result of chapter 2and 3, the design problem of the optimal guaranteed cost fuzzy controlleris formulated as a convex optimization. So that the closed-loopperformance can be no more than a certain upper bound in the presence ofplant uncertainties and the additive controller gain perturbations.