The Analysis Of Stability For Fuzzy Control

The analysis and design of controllers for fuzzy control systems have been an active question for a long time. It is very difficult of the stability for fuzzy control because of the systems' nonlinear. Now there have existed a lot of measures to ensure the stability of fuzzy control. However, more perfect methods are required eagerly. It is necessary to resolve theoretical problems of control more deeply.In recently years, Linear Matrix Inequality (LMI) has been used widely in control fields. As a convex method, with the method of interior point put forward, LMI becomes more and more important. Many problems of control can be transform feasible problems of linear matrix inequalities or convex problems with constraint of linear matrix inequalities. During solving problems of matrix inequalities, LMI is more useful than the equation of Lyapunov and Riccati. Moreover, The problems about matrix inequalities can be solved more easily due to the appearance of toolbox in MATLAB.This paper summarizes previous theories of stability forfuzzy control and describes characteristics and uses of LMI. The quadratic stability conditions of T-S fuzzy control systems of open-loop for continuous system and discrete system are concerned on the basis of Lyapunov theories. The stability conditions for closed-loop systems are given when there exist constraints. By the method of blocks, the problems of stability can be connected with robust control. The referred approaches that can relax quadratic stability conditions of fuzzy control systems are suggested based on LMI. They reduce the conservatism of previous theories by considering the interactions among the fuzzy subsystems in a matrix and solving it via LMIS. The examples and simulations can demonstrate the efficiency of the more relax approaches.