Controllability under positivity constraints of a size-structured population model with delayed birth process

Abstract

In this paper, we investigate the controllability under positivity constraints from the birth of a size-structured population system with delayed birth process. Firstly, we establish the well-posedness and positivity property of the model. Secondly, and more importantly, we derive a sufficient condition for boundary approximate controllability under state and control positivity constraints. The method relies on the feedback theory of infinite-dimensional positive systems.