The invariant discrete-time model of a continuous-time logistic system

This paper presents the invariant discrete-time model for a continuous-time system governed by the logistic differential equation. The state of this model matches that of the continuous-time original at the discrete-time instants for any sampling interval T. The model is obtained by converting the logistic equation into a linear one using state transformation and by applying to it the linear invariant model scheme. Simulations are carried out for the open-loop and closed-loop applications, where the proposed model is compared with other models, viz. the forward difference, Morishita, and Hirota Models, to show the superior performance of the proposed method.