Asymptotic Stability of Hessenberg Delay Diierential-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 yields the same linear delay ODE as the linearization of the state space form of the original problem, which is assured to be legitimate. Thus according to the theory of 6], the study of the asymptotic stability of the DDAE along the stationary solution can be transformed to the study of the null solution of the system obtained from the linearization of the original problem at the stationary solution by using the method of delay-essential-underlying-ODE introduced in 1]. We point out here that a similar method can be used to prove the validity of the direct linearization of delay diierential-algebraic equations of neutral type.