This paper deals with the design of a discrete time nonlinear observer for an anaerobic digestion process. The designed observer is devoted to a general class of systems, precisely linear systems, LPV systems with known and bounded parameters, and nonlinear Lipschitz systems. In order to ensure stability of the estimation error, a new LMI condition is proposed. In this LMI, additional decision variables are included to enhance its feasibility. Indeed, this was possible due to the use of a suitable reformulation of the Young’s inequality. Numerical simulations using the investigated two-step anaerobic digestion model show the effectiveness of the proposed LMI methodology.