Ecology, Environment and Conservation Paper

A FUZZY LOGIC CONTROL OF A POLYNOMIAL CARBON DIOXIDE MODEL

Azeddine Elmajidi, El housseine El Mazoudi, Jamila Elalami and Noureddine Elalami

Abstract

In this paper we investigated the stability property of the positive equilibrium for Lotka Volterra model, describing the interaction between carbon dioxide concentration, human population and forest biomass. By constructing a suitable Lyapunov function, a set of sufficient conditions which ensure the global asymptotical stability of the positive equilibrium is obtained. Then an attraction region of our model is defined. A Takagi–Sugeno multi-model first represents the studied model. Further, we developed a technique for designing an output feedback using the parallel distributed compensation method corresponding to this system. It permits to stabilize the atmospheric carbon dioxide around the reference equilibrium. The design conditions are given in linear matrix inequalities (LMIs) terms that can be solved efficiently using existing numerical tools. A numerical simulation is also carried out to support the analytical results.