A discrete-time nonlinear state observer for the anaerobic digestion process

This paper is concerned with the design of an LMI-based H-infinity discrete-time nonlinear state observer for an anaerobic digestion model. In presence of disturbances in both the dynamics of the model and the output measurement signals, the proposed observer robustly estimates all state variables including bacteria concentrations, which are costly and difficult to measure. In the goal to increase applicability of the proposed observer for other systems, we present the theoretical results in a general way. First, due to the use of Young's inequality in a convenient way, we get new sufficient conditions, expressed in terms of bilinear matrix inequalities (BMIs), ensuring the H-infinity criterion. Then, to render the BMIs convex, two alternative solutions are proposed, where both lead to linearmatrix inequality (LMI) conditions. It is shown analytically and numerically that these two solutions provide less conservative LMI conditions compared to the existing methods in the literature. To validate the proposed methodology on a real-world model, an application to an anaerobic digestion model is given.