Robust state feedback H∞ control for uncertain linear discrete singular systems

A linear matrix inequality (LMI) approach to the robust state feedback H_infin control for linear discrete singular systems with norm-bounded uncertainty is developed. By taking the relationship between slow and fast subsystems of a discrete singular system, a new bounded real lemma is proposed that proves to be sufficient and necessary. On the basis of this, the result on robust H_infin performance is obtained. An explicit expression for the desired controllers is also given that involves no system decomposition. The obtained results are formulated in terms of strict LMIs. Illustrative examples are provided to demonstrate the effectiveness of the proposed approaches.