Abstract
This paper is concerned with the initial conditions of an interconnected system that is composed of two linear implicit systems. For a single implicit system, an initial condition is called admissible if the system has a solution trajectory satisfying this condition. In the interconnected system, the set of admissible initial conditions of each sub-system may be reduced to a smaller subset due to the constraint imposed by the interconnection. We say that the admissible initial condition sets of the sub-systems are invariant under interconnection if they are not made smaller by interconnection. It is shown in this paper that the feedback and regular feedback structures of the interconnected system guarantee the invariance of the admissible initial condition sets under interconnection in the senses of impulsive-smooth distributions and usual smooth functions, respectively.
