Remarks on accessibility and oberservability of nonlinear implicit systems

Issue title: ISTET '01

Article type: Research Article

Authors: Schlacher, Kurt^{a; *} | Kugi, Andreas^b

Affiliations: [a] Johannes Kepler University Linz, Department of Automatic Control, and Control Systems Technology, Christian Doppler Laboratory for Automatic Control, of Mechatronic Systems in Steel Industries, Altenbergerstraße 69, A-4040 Linz, Austria | [b] Saarland University, Chair of System Theory and Automatic Control, PO Box 151150, D-66041 Saarbrücken, Germany

Correspondence: [*] Corresponding author. Tel.: +43 732 2468 9730; Fax: +43 732 2468 9734; E-mail: kurt.schlacher@jku.at

Abstract: This contribution presents tests, based on Lie-groups, for the accessibility and the observability of dynamic systems described by a set of implicit ordinary differential equations. It is shown that non-accessible or non-observable systems admit Lie-groups acting on their solutions such that distinguished parts of the system remain unchanged. The approach being presented requires the formal integrability of the system. Therefore, a short introduction to this theory is presented, as well as its application to systems of differential equations. Besides the theoretical results sketches for computer algebra based algorithms are presented that are necessary to perform the test for higher order systems.

DOI: 10.3233/JAE-2003-258

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 17, no. 1-3, pp. 121-132, 2003