Sliding mode observers for a class of uncertain differential-algebraic systems

This paper is concerned with the design of a sliding mode observer (SMO) for a class of uncertain nonlinear differential-algebraic systems (DAS) described by so-called semi-explicit forms with differential variables being coupled with algebraic variables. In order to estimate the algebraic variables directly, an improved algorithm is developed to reconstruct the algebraic variables that are subject to a singular distribution matrix of algebraic variables, using a series of elementary matrices followed by differentiation. An SMO is then designed based on the reconstructed algebraic variables in order to compensate for the effect of disturbances on estimation error dynamics such that the estimated states, including both the differential and algebraic variables, can follow the actual ones. The stability of the proposed observer is proven and an illustrative example is given to demonstrate the effectiveness of the improved algorithm for constructing the SMO.