The problems of stability, state feedback control and static Output feedback control fora class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled Strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static Output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach. (C) 2008 Elsevier Ltd. All rights reserved.