INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS

Systems of linear differential and algebraic equations occur in variou s ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics an d exact model matching. Differential/algebraic systems may represent a n input-output relation in a highly redundant way; still, it is often of interest to determine the input-output structure in terms of the or iginal parameters. This is the subject of the present paper. Specifica lly, explicit formulas in terms of original data will be given to answ er the following questions: Do the given equations determine a transfe r matrix, and if so, what is the pole/zero structure at infinity of th at transfer matrix? The approach is based on two characteristic sequen ces of subspaces, one in the input space and one in the output space.