Stability Analysis And Controller Design Of T-S Fuzzy Sampled-data Systems

The proposition and application of the T-S (Takagi-Sugeno) fuzzy model havetremendously extended the research field for fuzzy control theory. The principle ofthe universal approximation that a T-S fuzzy model can approximate any smoothnonlinear systems on any degree of accuracy made it feasible to analyze nonlinearsystem via T-S fuzzy model. And it has been demonstrated theoretically andpractically that this control method works effectively. Sampled-data behavior existsin almost all practical control systems. Thus the study of sampled-data system basedon T-S fuzzy model is of great practical importance.In this dissertation, the inputdelay approach is adopted to analyze T-S sampled-data system with/withoutcommunication delay. By means of Lyapunov stability theory, free-weighting matrixmethod, integral inequality and LMI method, some less conservative sufficientconditions for stability analysis and controller design are presented. The main workof this dissertation can be summarized as follows:The T-S sampled-data system without communication delay is first investigated.The communication delay can be omitted when controller is closed to the controlsystem. Based on the input delay approach, the hybrid fuzzy sampled-data system isconverted to a continuous fuzzy system with time-varying input delay, by means ofLyapunov-Krasovskii function, integral inequality and free-weighting matrixmethod, a stability condition and a stabilizing controller design condition in terms ofLMIs are obtained, which reduce the conservativeness of existing stability analysisand controller design method. The numerical simulations of inverted pendulum andtruck trailer are presented to further illustrate the effectiveness of the proposedmethod.Furthermore, this dissertation focuses on the stability analysis and controllerdesign issues for T-S fuzzy sampled-data systems with communication delay. Whenthe signal is transferred from controller to a remote control system, communicationswill be induced. The delay, either constant or varying, can degrade the performanceor even destabilize the control system. Based on the input delay approach, thehybrid fuzzy sampled-data system is converted to a continuous fuzzy system with atime-varying delay and a constant communication delay in input. A less conservativestability condition is obtained by integral inequality and free-weighting matrixmethod. According to the stability condition obtained above, a stabilizing controllerdesign method is proposed based on the BMI (Bilinear matrix inequality) method.Comparing with the existing results, much larger upper bound of sampling periodcan be acquired, which prove the condition in this paper is less conservative. Finally, numerical simulations of inverted pendulum and truck trailer show the advantageand effectiveness of the proposed method.