Observer-based fuzzy tracking control design for nonlinear uncertain descriptor dynamic systems

In this paper, a fuzzy logic controller with H
∞
tracking performance for uncertain nonlinear descriptor systems is proposed to attenuate the effects caused by unmodeled dynamics, disturbances, and approximation errors. First, the nonlinear descriptor system is represented by an equivalent Takagi-Sugeno type fuzzy model. Then, a state feedback fuzzy control scheme is developed to restrain the external disturbances such that the model reference H
∞
tracking performance is achieved. Furthermore, based on Lyapunov stability theorem, the proposed fuzzy control system can guarantee the stability of the whole closed-loop system and obtain good tracking performance as well. Stability conditions are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example of a nonlinear descriptor system control problem is given to illustrate the effectiveness of the proposed control scheme.