Asymptotic stability of Hessenberg delay differential-algebraic equations of retarded or neutral type

In this paper we prove that for Hessenberg delay DAEs of retarded type, the direct linearization along the stationary solution is valid. This validity is obtained by showing the equivalence between the direct linearization and the linearization of the state space form of the original problem, which is assured to be legitimate. Thus the study of the asymptotic stability of the stationary solution can be transformed to the study of the null solution of the linearization of the original problem. We point out here that a similar method can be used to prove the validity of the direct linearization of delay differential-algebraic equations of neutral type. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.