Robust stabilization for a class of uncertain discrete-time singular systems with time-delays

The robust stabilization via state feedback for class discrete-time singular systems with norm-bounded parameter uncertainties is discussed. Under a series of equivalent transformation, the equivalence between this problem and the robust stabilization via state feedback for uncertain standard state-space discrete-time linear systems with time-delays is obtained. In terms of LMI, a necessary and sufficient condition that there exists a robust state feedback stabilizing controller for all admissible uncertainties is given, the design method of the memoryless state feedback controller and a controller is also given.