SearchPublisher and Institutes
You are here: Home :: Area NEM :: Engineering :: Automation
Kurt Schlacher, Kurt Zehetleitner
A Formal Approach for Implicit Dynamic Systems
The modelling of complex systems leads often to sets of algebraic and ordinary differential equations. This contribution presents methods for implicit systems based on the formal theory of ordinary differential equations. It will be shown that certain implicit systems, also called formally integrable, offer properties, which permit many investigations without being transformed to the explicit form. Here, a dynamic system is identified with a submanifold with a certain geometric structure. The form of the equations corresponds merely to a special parametrization of this submanifold. Since any implicit system can be transformed to a formally integrable one, provided certain regularity conditions are met, this type of system appears to be a connecting link between explicit and implicit systems. Based on this consideration we present results for the general case, investigate systems, which are linear in the derivatives, in more detail, and finish with the application of the theory to the linear and time invariant case.
at – Automatisierungstechnik, Oldenbourg Wissenschaftsverlag
Print ISSN: 0178-2312
Volume: 52, 09/2004
Pages: 446 - 455