An LMI approach to robust stabilization for uncertain discrete-time singular systems

The robust stabilization via state feedback for discrete-time singular systems with norm-bounded time-invariant parameter uncertainties in the matrix E is discussed. Without the regularity of the systems, the equivalence between this problem and the robust stabilization via state feedback for uncertain standard statespace discrete-time linear systems is obtained. In terms of LMI, a necessary and sufficient condition that there exists a robust state feedback stabilizing controller such that the closed-loop system is regular, causal and stable for all admissible uncertainties is given, the design method of the controller and a controller are also given.