Admissibility analysis for discrete-time bilinear singular systems using bilinear state-feedback controller

In this paper, both the admissibility analysis and the stabilization of discrete-time bilinear singular systems are addressed, respectively. First, a sufficient condition of admissibility of discrete-time singular system is derived. Then by applying the matrix inequality, a bilinear state-feedback controller is designed to guarantee the closed-loop discrete- time singular bilinear systems to be admissible. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) to derive a single-step LMI condition for bilinear state-feedback controller design is presented. Finally, a numerical example is provided to demonstrate the effectiveness of the method proposed in this paper.