Extended Luenberger-type State Observer Design for a Class of Semilinear PDE Systems

This paper is concerned with the design of an extended Luenberger-type state observer for a class of one-dimensional multi-state semilinear PDE systems considering distributed in-domain measurements over the spatial domain. A design based on modal assignment is proposed for the stabilization of the estimation error dynamics. The approach uses the Riesz spectral characterization of the system differential state operator and the local Lipschitz constant related to the non-linearity of the mathematical model. Thus, the synthesis conditions are reduced to the feasibility of a set of LMI constraints which can be solved numerically using semi-definite programming (SDP) tools. The performance of the observer is exemplified through numerical experiments which demonstrate the efficiency of the proposed approach. A case study consisting of an isothermal tubular reactor is presented to demonstrate the observer performance which are evaluated through simulation studies.