By using matrix inequality method and singular Liapunov function, H∞ state feedback control problem for a discrete singular system is studied. A necessary and sufficient condition for the system to be regular, and satisfy a prescribed H∞-nom condition is obtained and a admissible state feedback controller is given. The second, the H2 performance criterion for a class of uncertain discrete singular systems are discussed, the admissible uncertainty are norm-bounded. A sufficient condition for an uncertain discrete singular system to be regular, causal, stable and possess H2 performance criterion is given.

singular Liapunov function; H∞ control; matrix inequality; uncertain discrete singular system; H2 performance criterion