The robust stability of discrete-time uncertain singular systems is investigated with the method of linear matrix inequality(LMI). Two sufficient conditions for robust stability of discrete-time uncertain singular systems with polytope type uncertainties are proposed. These conditions are expressed in terms of a set of linear matrix inequalities (LMIs) involving only the vertices of the polytope domain. It enables us to determine robust stability of discrete-time uncertain singular systems easily by solving some LMIs. The new approaches can yield much sharper and less conservative results than the simultaneous stability approaches. Furthermore, the controller is designed to guarantee that the closed loop system is regular, causal and stable for a class of discrete-time uncertain singular systems with polytope type uncertainties. A numerical example is included to illustrate the the efficiency of the proposed approaches.

robust stability;discrete-time singular system;linear matrix inequality(LMI);parameter-dependent Lyapunov matrix