Exponential stabilization of dynamic systems by state feedback control of linear

In this paper, we consider a stage structured model of a harvested fish population. The model is a continous-time system involving a nonlinear recruitment function. Using the generalization of Gronwall-Bellman lemma, we show how to act on the fishing effort in order to prevent the extinction of the population. More precisely, we show how to compute the fishing effort as a feedback control in order to maintain the fish population state around a desired steady state. we find a sufficient condition for our nonlinear system to be stabilizable by state feedback control.