The structure of the singularities of holomorphic matrices

Abstract

SynopsisIn this paper we consider a holomorphic matrix H(z) over a possibly unbounded region Ω and we study its properties in the neighbourhoods of a boundary point z0 of Ω (it may be z0 = ∞ if Ω is unbounded and z0 may not be an isolated singularity). Applications to systems theory and, in particular, to the theory of delay systems are presented. In this case the properties of completability, small solutions observability and zeros at z0 = ∞ are investigated.