This paper investigates the problem of positive stabilizability of single-input LTI positive systems. Firstly, for a single-input continuous-time positive linear system, it has been derived that a necessary condition of the existence of a stablilizing linear time-invariant controller is the number of nonnegative real poles not being greater than one. Inspired by that, the continuous-time positive stabilizability of systems with unstable complex poles is studied in this paper, where the third-order and higher-order cases are considered. Secondly, an enhanced method to construct the static state-feedback gain of a sampled positive system is presented, which takes account of the positivity preservation in the sampling interval. According to the method, the positive stabilizablity of the single-input second-order sampled positive system is analyzed. Some numerical examples are finally presented to illustrate the theoretical results.

No abstract