Positive stabilization of singular systems by proportional derivative state feedback

Abstract

This paper considers the problem of positive stabilization of linear continuous-time singular systems by both proportional and proportional derivative state feedback. First, we provide conditions for a singular system to be admissible (stable, regular, and impulse-free). Then, with the aid of these conditions, we 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. Two design strategies are given for positive stabilization by proportional derivative state feedback with the aid of normalization of singular systems. Numerical examples are provided to support the theoretical results.