摘要：AbstractEarly stages modelling of processes involves issues of classification of variables into inputs, outputs and internal variables, referred to as Model Orientation Problem (MOP) which may be addressed on state space implicit, or matrix pencil descriptions. Defining orientation is equivalent to producing state space models of the regular or singular type. In this paper we consider autonomous differential descriptions defined by matrix pencils and then search for strict equivalence transformations which introduce the partitioning of the implicit vector into states and possible inputs and outputs, referred to as system orientation. The Kronecker invariant structure of the matrix pencil description is shown to be central to the solution of system orientation and this is expressed as a problem of classification and partitioning of the Kronecker invariants. It is shown that the types of Kronecker invariants characterise the nature of the system orientation solutions. Studying the conditions, under which such oriented models may be derived, as well as their structural properties in terms of the Kronecker structure, is the issue considered here.
