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

摘要

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