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A Lyapunov approach to the stabilization of a harvested fish population model

El Houssine El Mazoudi, Noureddine Elalami, Mostafa Mrabti

This study describes the results of an application of control engineering methodology to the problems of regulating fisheries. By employing a wellknown lyapunov approach, we develop a technique for designing a state feedback control law which stabilizes the system. The continuous agestructured model is considered. The fishing effort is taken as a control term the age classes as a states and the total caught as a measured output. we interest in the design of a fishing strategy by constructing a linear feedback control lawwhich can be extended to an output static feedback that permits to stabilize the studied systemaround a nontrivial steady state.Asufficient condition for stabilization via Lyapunov function is given. Numerical examples are indicated.