Dissipation Analysis And Synthesis Of Several Classes Of T-S Fuzzy System

The dissipation exists in the dynamic process of systems as the property of input and output generally. It reflects the energy attenuation characteristics of systems under tolerated input conditions. The research about dissipation of linear systems have driven to maturity stage in recent decades, but that of nonlinear systems are lack of theoretical investigation by the reason of the systems’complexity and variability. T-S fuzzy systems can describe the complex nonlinear systems by a group of fuzzy set; also it can approximate the continuous function in n-dimensional Euclidean space by any degree of accuracy. The achievements about stability analysis of nonlinear systems by T-S fuzzy control technique attracted much attention. However, when it comes to engineering practice, it is difficult to find the public positive-definite matrix P in the establishment of Lyapunov function because of the large numbers of rules. Based on the above issues, the property of T-S fuzzy systems whose input with dual overlapping fuzzy partition to establish piecewise fuzzy Lyapunov function are used, and then sufficient conditions of strictly dissipation for several classes of T-S fuzzy systems will be given. These conditions only need finding public positive-definite matrixes in every maximum overlapped group and making full use of the information of membership functions to reduce the difficult of finding the public positive-definite matrix P. Furthermore, using parallel distributed compensation (PDC) and linear matrix inequalities (LM1) approaches to investigate the dissipation of the closed-loop systems and controller design method, and finally the state feedback controller design of the fuzzy systems will be obtain. The main content can divide into the following seven parts:(1) The perface has given an overview about the development and research of dissipation theory, basic thought and application background of dissipation theory, fuzzy systems, T-S fuzzy systems and then illustrated the main work and the significance of research in this thesis. (2) There are some prerequisites needed to be introduced. The basics of fuzzy mathematics, T-S fuzzy descriptor systems, the definition and properties of dual overlapping partition, the relevant knowledge of piecewise fuzzy Lyapunov function, the parallel distributed compensation method and linear matrix inequalities.(3) Firstly, We have established the model of continuous-time T-S fuzzy regular systems whose input with dual overlapping fuzzy partition. Then we respectively find public positive-definite matrix P in every maximum overlapped group and define piecewise fuzzy Lyapunov function. According to the definition of dissipation, we have analyzed the sufficient condition of tolerant and strictly dissipative for the autonomous systems. Furthermore, we have designed the state feedback controller using PDC scheme, and obtain the dissipation of the closed-loop systems. After each theorem we will give two inferences for strictly passive and H∞control with a strictly norm bound y. We also analyze the sufficient condition of strictly dissipative for the closed-loop systems.Finally, numerical simulation has been presented to illustrate the feasibility of the proposed methods.(4) For a class of uncertain T-S fuzzy systems whose input with dual overlapping fuzzy partition, we develop the piecewise fuzzy Lyapunov function. Then we have analyzed the sufficient condition of the closed-loop systems and rubost strictly dissipative for those systems. Furthermore, we have designed state feedback controller using PDC scheme and presented the sufficient condition for the existence of the controller in the form of LMI.(5) We have established the model of descriptor continuous-time T-S fuzzy systems whose input with dual overlapping fuzzy partition. Then the sufficient condition of tolerant and robust strictly dissipative for the T-S fuzzy descriptor systems has been presented. This condition makes full use of the information of membership functions and respectively finds public positive-definite matrixes in every maximum overlapped group. Based on this, the design of state feedback controller has been given. Furthermore, the sufficient condition for the existence of the controller in the form of LMI has been presented. Finally, numerical simulation has been presented to illustrate the feasibility of the proposed methods.(6) For a class of uncertain T-S fuzzy descriptor systems whose input with dual overlapping fuzzy partition, we develop the piecewise fuzzy Lyapunov function. Then the sufficient condition of the closed-loop systems and robust strictly dissipative for those systems have been analyzed. Furthermore, state feedback controller has been designed by using PDC scheme and the sufficient condition for the existence of the controller in the form of LMI has been presented.(7) Finally, summarized the main work of this thesis. Meanwhile, an expectation for the future research has been proposed.