Model reduction for a class of linear descriptor systems

For linear descriptor systems of the form Bẋ=Ax+Cu, y=Ox, this paper constructs reduced order systems associated with a given part of the finite spectrum of the pencil P(λ)=A−λB. It is known that the reduction can be obtained by a block diagonalization of the generalized Schur decomposition of P(λ). In this paper we consider the special case when B=[H000]and A=[JG−F∗0]. This case is suited, in particular, for linearized hydrodynamic problems. We derive a sufficient condition under which the reduced system can approximate the initial one and show that it can be obtained in significantly cheap and efficient approaches. We consider first in detail the case when F=G and H is the identity matrix and then treat the general case.