Robust control for discrete-time fuzzy descriptor system with time-delay

In this paper, the robust stability and stabilization problems are investigated for a class of uncertain discrete-time T-S fuzzy descriptor system with time-delay. In terms of strict linear matrix inequality and without requiring any system model transformation, a delay-dependent criterion for the systems to be admissible is obtained. Based on the criterion, an admissible state feedback controller is constructed, which guarantees that, for all admissible uncertainties, the resulting closed-loop system is regular, causal and stable. An explicit expression for the desired controller is also given, which involves no matrix decomposition. Finally, a numerical example is introduced to demonstrate the validity and applicability of the proposed results.