Redundancy approach for fuzzy Lyapunov stabilization of Takagi-Sugeno descriptors

This paper presents new stability conditions for Takagi-Sugeno (T-S) descriptors. Thanks to the descriptor redundancy, LMI based controller design of less conservatism are derived. These conditions are obtained using a fuzzy Non Quadratic Lyapunov function (NQLF) approach with a non-Parallel-Distributed-Compensation (Non-PDC) control law. First, stabilization without constraints is considered for the sake of genericity. Then, H∞ based controller design is proposed in order to deal with the stability of closed loop descriptors subject to external disturbances. Finally, a numerical example is proposed to illustrate the efficiency of the proposed approaches.