Structure at Infinity of Structured Descriptor Systems and Its Applications
Kazuo Murota, Jacob W. van der Woude · SIAM Journal on Control and Optimization · 1991
The generic structure at infinity of the transfer matrix of a descriptor system is investigated under the physically reasonable assumption that the coefficients in the equations are classified into independent physical parameters and dimensionless constants. For such a structured descriptor system, the generic structure at infinity is characterized in terms of an independent assignment (or weighted matroid intersection) problem. This leads to necessary and sufficient conditions for the generic solvability of the exact matching problem for a (singular) descriptor system and for the generic solvability of the disturbance decoupling problem for a nonsingular descriptor system. The obtained conditions can be checked by efficient matroid-theoretic algorithms.