Constant-gain nonlinear adaptive observers revisited: an application to chemostat systems

This study deals with constant-gain adaptive observers for nonlinear systems,for which relatively few solutions are available for some particular cases.We introduce an asymptotic observer of constant gain for nonlinear systems that have linear input.This allows the observer design to be formulated within the linear matrix inequality paradigm provided that a strictly positive real condition bet ween the inpu t disturbance and the output is fulfilled.The proposed observer is t hen applied to a large class of nonlinear chemos tat dynamical systems that are widely used in the fermentation process,cell cultures,medicine,etc.In fact,under standard practical assumptions,the necessary change of the chemos tat state coordinates exis ts,allowing use of the const ant-gain observer.Finally,the developed theory is illustrated by estimating pollutant concentration in a Spirulina maxima wastewater treatment facility.