H∞ Trajectory Tracking Control for Fuzzy Descriptor Systems

In this paper, we consider model reference H(infinity) trajectory tracking control of nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy descriptor systems. The descriptor system describes a wider class of systems and the standard state-space systems representation is a special case of descriptor systems. The dynamics of the given nonlinear system are represented by a fuzzy descriptor system and the design is carried out with a quadratic Lyapunov function. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for satisfying the given H(infinity) tracking performance. Furthermore, the stability of the closed loop system is also ensured. The advantage of descriptor system based approach is that the number of LMI conditions for designing a controller is less than the state-space approach. Finally, a simulation example for controlling system using fuzzy descriptor system is presented to illustrate the effectiveness of the proposed control scheme.