The Research Of Piecewise Fuzzy Control For Nonlinear Systems

The stability analysis and systematic design of Takagi-Sugeno (T-S) fuzzy systems are a hotspot in the fuzzy control field. Based on the Lyapunov direct method, linear matrix inequalities(LMI) and parallel distributed compensation (PDC),a lot of research applications have been gained on T-S fuzzy systems. A common positive-definite matrix P must be found to satisfy the equations. For actual control objects of engineering application, the difficulty to solve LMI will be increased due to the large number of premise variables and rules of fuzzy systems.For the conservativeness of solving LMI, many scholars have been studying the structure of the Lyapunov function, and getting the non-single Lyapunov function method. Nevertheless, few reasearch on continuous T-S fuzzy systems is done with this method.Based on the structure analysis of common quaratic Lyapunov function (CQLF), the piecewise quaratic Lyapunov function (PQLF) and fuzzy Lyapunov function (FLF) are constructed respectively with the membership function structure and fuzzy rule premises of T-S fuzzy systems, and the piecewise fuzzy Lyapunov function(PFLF) is defined by bring the FLF into the piecewise fuzzy regions educed by PQLF. This paper deals with the farther analysis and research for the continuous T-S fuzzy systems with single(CQLF) and non-single Lyapunov functions(PQLF,FLFå'ŒPFLF).Firstly, this paper deals with the analysis of stabilization and the design of controllers of T-S fuzzy systems.Single and non-single robust controllers are studied by utilizing the single and non-single Lyapunov functions, and the parametric methods of robust controllers are given in the form of LMI. Secondly, based on T-S fuzzy systems with parametric uncertainties, the sufficient conditions for fuzzy guaranteed cost controller and piecewise fuzzy H∞state feedback controller are derived by making use of non-single Lyapunov functions, and these controllers are given in the form of LMI. Finally, the problems of piecewise guaranteed cost controller and piecewise fuzzy output tracking control are studied, and the sufficient conditions for the gradually stabilization of T-S fuzzy systems with parametric uncertainties and time-delay are given.Simulating the control systems designed by these different approaches respectively, the results shows that the controllers based on PFLF have better control performance than other approaches, and it reduces the conservativeness of solving LMI due to a large number of premise variables and rules of a fuzzy system.