Multimodel robust observer for an uncertain fish population model

• A new design of observer is given for a nonlinear and uncertain biological system.
• To estimate the stock state and biomass, an observer is built under LMI formulation.
• The convergence condition is given using the 2nd method of Lyapunov and an L2L2 approach.
• The estimation error converges to zero, & the estimated state tracks the actual state.
• The proposed method is robust against modelling uncertainties and measurement noise.

In this paper, a new method is proposed to design an observer for a nonlinear and uncertain system describing a continuous stage structured model of a harvested fish population. The aim is to get an estimation of the biomass of fishes by stage class. In the studied model the fishing effort is considered as a control term, the stage classes as states and the quantity of captured fish as a measured output. A Takagi–Sugeno multimodel first represents the uncertain non-linear model. Next, we develop a technique for designing a multimodel observer corresponding to this system, which attenuates the effect of modelling uncertainties and measurement noise on the state estimation. The design conditions are given in linear matrix inequalities (LMIs) terms that can be solved efficiently using existing numerical tools. The validity of the proposed method is illustrated by the simulation results.