The behavioural pole structure of nD systems

We discuss the pole structure of nD linear systems from a behavioural point of view. We define the notions of irreducible, reducible, manifest and latent poles, which correspond in the classical 1D setting to controllable poles, input decoupling zeros, observable poles and output decoupling zeros. Our definition of poles can be interpreted in terms of kernel representations, and also allows an integral representation of any zero-input trajectory in terms of system poles