Abstract
Using translated X-factorable phase space transformations and nonlinear variable transformations a dynamically similar linear ODE model is associated to the Lotka-Volterra system models with a positive equilibrium point. This enables to use a linear full state feedback controller to stabilize the system in controllable cases, that leaves the open loop equilibrium point unchanged. The linear state feedback controller design problem in the general case has also been formulated to ensure the compartmental property of the closed loop system from which the existence of a diagonal Lyapunov function follows. Further extension has been obtained by using the time re-parametrization transformation defined for quasi-polynomial models.
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