Adaptive and robust controller design for uncertain nonlinear systems via fuzzy modeling approach

The issue for designing robust adaptive stabilizing controllers for nonlinear systems in Takagi-Sugeno fuzzy model with both parameter uncertainties and external disturbances is studied in this paper. It is assumed that the parameter uncertainties are norm-bounded and may be of some structure properties and that the external disturbances satisfy matching conditions and, besides, are also norm-bounded, but the bounds of the external disturbances are not necessarily known. Two adaptive controllers are developed based on linear matrix inequality technique and it is shown that the controllers can guarantee the state variables of the closed loop system to converge, globally, uniformly and exponentially, to a ball in the state space with any pre-specified convergence rate. Furthermore, the radius of the ball can also be designed to be as small as desired by tuning the controller parameters. The effectiveness of our approach is verified by its application in the control of a continuous stirred tank reactor.