LMI-based $\mathcal{H}_{\infty}$ nonlinear state observer design for anaerobic digestion model

Khadidja Chaib Draa (1, 2) , Holger Voos (1) , Marouane Alma (2) , Ali Zemouche (2, 3) , Mohamed Darouach (2)

1 SnT - Interdisciplinary Centre for Security, Reliability and Trust [Luxembourg]
2 CRAN - Centre de Recherche en Automatique de Nancy
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

This note deals with the design of an H_infty nonlinear state observer for the anaerobic digestion model. Positively, the designed observer is an unified one that can be used for different class of systems, mainly linear systems, Linear Parameter Varying (LPV) systems with known and bounded parameters, and nonlinear Lipschitz systems. Applying the Lyapunov theory and the H_infty criterion, Linear Matrix Inequality (LMI) condition is synthesised and solved to obtain the designed observer gains. The novelty of our work consists in the relaxation of the synthesized LMI condition through the inclusion of additional decision variables. This was possible due to the use of a suitable reformulation of the Young’s inequality. Stability, effectiveness and potency of the theoretical results are confirmed by the simulation results.

Mots clés: Anaerobic digestion; LMIs; Observer design; Nonlinear systems; H ∞ Criterion

Domaines: Automatique

Khadidja Chaib Draa, Holger Voos, Marouane Alma, Ali Zemouche, Mohamed Darouach. LMI-based $\mathcal{H}_{\infty}$ nonlinear state observer design for anaerobic digestion model. 25th Mediterranean Conference on Control and Automation, MED 2017, Jul 2017, Valletta, Malta. ⟨10.1109/med.2017.7984196⟩. ⟨hal-01567357⟩