On the positive stabilizability of sampled positive systems

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.