An LMI approach to DD-stability and DD-stabilization of linear discrete singular systems with state delay

The problems of DD-stability and DD-stabilization for linear discrete singular systems with state delay are addressed in this paper. By using the state augmentation technique, a necessary and sufficient DD-stability condition and a sufficient DD-stabilization condition for linear discrete singular time-delay systems are firstly proposed. Then, based on these conditions, quadratic DD-stability and DD-stabilization conditions for linear discrete singular time-delay systems with norm-bounded uncertainties and interval uncertainties are obtained, respectively. Both the DD-stability and DD-stabilization conditions are proposed in terms of linear matrix inequalities. Finally, illustrative examples show that the proposed conditions are effective to check the DD-stability and to design the DD-stabilizing controller for linear discrete singular time-delay systems.