Brief paper: lmi-based H∞ control for linear singular discrete systems: a novel method

This study investigates the problem of state feedback H_∞ control for linear singular discrete systems. First, a novel admissibility condition and then a new bounded real lemma are proposed for linear singular discrete systems. Then, the existence condition and explicit expression of a desirable state feedback H_∞ controller are obtained based on the above results. It should be pointed out that all the conditions in this study are necessary and sufficient and in the form of strict linear matrix inequalities that can be solved easily. Finally, some numerical examples are provided to illustrate the effectiveness of the theoretical results in this study.