Positive Stabilization of Linear Continuous-Time Singular Systems

This paper considers the problem of positive stabilization of linear continuous-time singular systems by state feedback. First, necessary and sufficient conditions for a singular system to be admissible (stable, regular, and impulse-free) are given in terms of LMI. Based on this result, the state feedback admissibility problem is solved without positivity constraints. Then, it is shown that the LMI based stabilization results of singular systems can conveniently be combined with positivity constraints to establish positive stabilization of general singular systems. We also show that the well-known positive stabilization technique based on LMI for conventional linear systems can be applied to singular systems represented by its standard decomposition form. Numerical examples are provided to support the theoretical results.