Time Delay Stability Analysis Of Fuzzy System And H-infinity Control

Present-day physical, engineering and social systems are generally of highdimensions and processing interacting dynamic phenomena. The information processingand requirements to experiment with these models for control purpose are frequentlyexcessive. As a consequence, the methodologies of large-scale interconnected systemstheory provide techniques through the manipulation of a system structure in some wayto overcome this problem. In the large-scale system model, compared with linearlarge-scale systems, it is more difficult to analyze nonlinear processes. As we know, T-Sfuzzy model has been recognized as a powerful tool in approximating complexnonlinear systems and then a fuzzy controller can be designed to control the T-S fuzzymodel. On the other hand, real systems with time delays are common in biology,mechanics and economics. Moreover, time-varying delay is more crucial and universalin real engineering processes and has more complex impacts on system dynamics thanconstant delay. Since time delay is a main factor of instability of time-delay systems, theissue of stability analysis of time-delay systems has been one of the main concerns ofresearchers.By large-scale system theory and fuzzy system theory, in this assignment, weanalyze the stability of discrete-time and continuous-time fuzzy systems withtime-varying delays, respectively, and design the fuzzy controller. The main content isorganized as follows:1) According to discrete-time fuzzy large-scale system with time-varying delays,we propose the fuzzy mathematic model. Based on Lyapunov stability theory, weanalyze the stability of the system by introducing piecewise quadratic functional and animproved free weighting matrix.2) We design the H∞controller of discrete-time fuzzy large-scale system withtime-varying delays, which is less conservative and more powerful than the existingapproaches based on the common quadratic LKF.3) According to continuous-time fuzzy large-scale system with time-varying delays,we propose the fuzzy mathematic model. Based on T-S fuzzy model and Lyapunov-krasovskii functional, we analyze the stability of the system by introducingpiecewise quadratic functional and an improved free weighting matrix.4) We bring forward H∞controller design of the continuous-time fuzzylarge-scale system with time-varying delays, which is less conservative and morepowerful than the existing approaches based on the common LKF.All these works mentioned above are tested through MATLAB simulation. It isdemonstrated via examples that the decentralized H∞state feedback controllers areefficient in solving the stability problems of both the discrete-time and continuous-timefuzzy large-scale systems with time delays.