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

Abstract

Abstract 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.