  This paper studies linear time-invariant descriptor systems which are not
necessarily regular. We introduce the notion of partial detectability and
characterize this concept by means of a simple rank criterion involving the
system coefficient matrices. Three particular cases of this characterization
are discussed in detail. Furthermore, we show that partial detectability is
necessary for the existence of a generalized functional observer, but not
sufficient. We identify a condition which together with partial detectability
gives sufficiency.

Optimization and Control