A feedback control law to stabilise a harvested fish population system

In this paper, we consider the problem of stabilising a continuous fish population system via a state feedback control. The model considered is structured in n age classes and includes a non-linear stock-recruitment relationship. In our case, the variation of the fishing effort is used as a control term, the age classes as states and the quantity of captured fish per unit of effort as a measured output. The back stepping approach is employed to stabilise the studied system around a reference equilibrium point. Explicit expression of a bounded fishing effort and a Lyapunov function are given. An example is tested to illustrate the applicability of the proposed technique.