Strict LMI conditions for stability and stabilization of discrete-time descriptor systems

For linear discrete-time descriptor systems, we consider stability and stabilization conditions using matrix inequality approach. We present a new strict linear matrix inequality (LMI) condition which is necessary and sufficient for stability of unforced descriptor systems. Then, we use the condition to consider stabilization problem by descriptor variable feedback and static output feedback. By introducing a new matrix variable with certain structure, we establish sufficient conditions in form of strict LMI for stabilizing controller design.