Controller Design for Discrete-Time Descriptor Models: A Systematic LMI Approach

This paper provides a systematic way to generalize the controller design for discrete-time nonlinear descriptor models. The controller synthesis is done using a Takagi-Sugeno representation of the descriptor models and linear matrix inequalities. We propose approaches to exploit the discrete-time nature of the problem by using delayed Lyapunov functions, which allow delayed controller gains. In addition, the well-known Finsler's Lemma is used to avoid the explicit substitution of the closed-loop dynamics. Examples are provided to show the effectiveness of the proposed results.