New Study on a Necessary and Sufficient State-Feedback Stabilization Condition for Singular Discrete-Time System

This paper proposes a new necessary and sufficient condition for the state-feedback stabilization of discrete-time singular systems via a linear matrix inequality (LMI) approach. This paper derives an alternative form of admissibility criterion of the discrete-time singular systems as a necessary and sufficient condition. Then, for the closed-loop system obtained by using the state-feedback controller, the derived admissibility criterion is applied, which leads to the non-convex matrix inequalities. This paper specially chooses the block entries of the congruent transformation matrix so that the non-convex matrix inequalities are successfully converted into the convex one. Consequently, the state-feedback stabilization control for discrete-time singular systems is obtained as a necessary and sufficient condition in terms of LMIs. The feasibility of the proposed control is further described via a numerical example.