H∞ Tracking Performance Design for Fuzzy-Model-Based Descriptor Systems Subject to Parameter Uncertainties

This paper presents the stability and H∞ tracking performance design of a fuzzy-model-based descriptor system 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 fuzzy observer-based state feedback control scheme is developed to restrain the external disturbances such that the 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 show the validity and confirm the performance of the proposed scheme.