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Orientation of Implicit State Space Models and the Partitioning of Kronecker Structure

Karcanias, N., Vafiadis, D. & Livada, M. ORCID: 0000-0002-0432-872X (2021). Orientation of Implicit State Space Models and the Partitioning of Kronecker Structure. In: IFAC-PapersOnLine. 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020, 23-27 Aug 2021, Online. doi: 10.1016/j.ifacol.2021.06.069


Early 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.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: Copyright © 2021 The authors. This is an open access article under the CC BY-NC-ND license.
Publisher Keywords: state-space; singular systems; Kronecker form; matrix pencils; system orientation
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
T Technology > TJ Mechanical engineering and machinery
Departments: School of Science & Technology > Engineering
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