LMI-based invariant like nonlinear state observer for anaerobic digestion model

This note deals with the design of an invariant like nonlinear state observer for a two step (acidogenesis-methanogenesis) mass balance nonlinear model. In order to ensure the stability of the estimation error, a new LMI condition is proposed. The feasibility of this LMI is enhanced due to the use of a suitable reformulation of the Youngs inequality. Actually, additional decision variables are included in the LMI to render its feasibility less conservative compared to those established in the literature for the same class of systems. The numerical simulations using the investigated anaerobic digestion model show the effectiveness of the proposed LMI methodology.