On the positive stabilizability of sampled positive systems

Abstract

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.

On the reduced conditions for positive consensus of second‐order multi‐agent systems

“…Therefore, in this paper, the positive consensus of homogeneous MASs with single‐input second‐order individual dynamics is investigated, where double‐input cases are omitted as the corresponding positive MAS can always reach a consensus. In our previous work [27], the positive stabilizability of linear positive systems is discussed, which is proved to be a necessary condition on the solvability of positivity‐preserving consensus problems in this paper. For undirected topologies, necessary and sufficient conditions of continuous‐time and discrete‐time cases are derived to solve the positivity‐preserving consensus problems, which are just with respect to the smallest or/and the largest nonzero eigenvalues of the Laplacian matrices.…”

Finite time stability analysis for T-S fuzzy positive systems and its application in pest control

“…Hence, positive systems have received extensive attentions. Recently, some important results on positive systems have been published, such as controller synthesis [1][2][3], stability analysis [4][5] and 1 L -gain analysis [6][7].…”