An LMI-Based H ∞ Discrete-Time Nonlinear State Observer Design for an Anaerobic Digestion Model

Abstract This paper is devoted to the design of an H ∞ discrete-time nonlinear state observer for an anaerobic digestion model. Indeed, the designed observer can be used for different class of systems, mainly linear systems, LPV systems with known and bounded parameters, and nonlinear Lipschitz systems. We use an LMI approach to guarantee the H ∞ asymptotic stability of the estimation error despite the disturbances affecting the system dynamics and measurements. The synthesised LMI is relaxed due to the inclusion of additional decision variables which enhance its feasibility. This was possible due to the use of a suitable reformulation of the Young’s inequality. Simulation results are given to show the robustness of the designed observer.