Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach

The output tracking control problem for nonlinear systems in the existence of both parameter perturbations and external disturbances is studied in this paper. Our approach is based on Takagi-Sugeno (T-S) fuzzy modeling method and variable structure control (VSC) technique. Therefore, the systems considered in this paper are not and need not be in the triangular and parametric strict-feedback form, which are prevalent among adaptive model following control for nonlinear systems, or in the normal form, which pervades almost all the existing results in neuro-fuzzy model following control approach. To make a preliminary, we first study the problem of stabilization of T-S fuzzy systems by using a VSC technique. A method for the design of switching surface based on linear matrix inequalities is developed and a stabilizing controller based on reaching law concept in the existence of both parameter perturbations and external disturbances is proposed. Then, the method is extended to design the controllers for output tracking of T-S fuzzy nonlinear systems in two cases, i.e., the systems which possess the so-called strong passive subsystems and strong stable zero dynamics, respectively. Finally, illustrative examples are presented to demonstrate the whole design procedure in using our approaches from the very beginning with the original nonlinear systems to their fuzzification and finally to the working out of the desired controllers. Simulation results show that the goal of output tracking can be achieved by the proposed controllers.