Admissibility Analysis and Robust Stabilization via State Feedback for Uncertain T-S Fuzzy Descriptor Systems

This paper considers the admissibility and robust stabilization via state feedback for continuous-time T-S fuzzy descriptor systems (TSFDS) with a class of uncertainties. First, the admissibility of the nominal system without uncertainties is investigated. An equivalent augmented system is presented to deal with different and singular derivative matrices. Then, admissible conditions for the open-loop and close-loop systems are both derived based on a non-quadratic fuzzy Lyapunov function. Second, the admissibility and robust stabilization of TSFDS with uncertainties in all matrices are investigated. The uncertainty in each derivative matrix is equivalently expressed by a constant matrix left multiplied by an invertible uncertain matrix so that a similar augmented system can be constructed. Then admissible conditions are derived. This paper generalizes existing related results since we consider a wider class of TSFDS with different derivative matrices and different membership functions in each subsystem. All conditions are expressed as strict linear matrix inequalities (LMIs). Finally, a simulation example is provided to show effectiveness of the proposed results.