Chained aggregation of singular systems

Extends the notion of aggregation to singular systems (sE-A). Necessary and sufficient conditions for complete aggregability are given which reduce in the state-space case, E=I, to Aoki´s conditions. A geometric quotient-space analysis is given which uses a new result on the pencil induced in the quotient space by a regular matrix pencil. A generalized chained aggregation algorithm is used to put the system into a Hessenberg form which provides a reduced-order model for the output dynamics. It is shown that, as in the state-space situation, chained aggregation corresponds to removal of the unobservable subspace. It is also pointed out that the usual state-space chained aggregation algorithm is very efficient and numerically unstable. Specializing the singular system chained aggregation algorithm to the state-space case yields a better and more streamlined approach