Observer design for a class of differential-algebraic systems

This paper deals with the design of a Luenberger-like observers in a class of nonlinear differential-algebraic systems (DAS) described by the so-called semi-explicit forms with the differential variables being coupled with algebraic variables. The key point of designing the observer for the DAS is the reconstruction of the algebraic variables because its distribution matrix is singular. The reconstruction consists of a serial elementary matrices followed by differentiation such that the algebraic variables can be directly estimated in the observer. The stability of the proposed observer is proved and an illustrative example and simulations are given to describe the design of the observer.