Linear differential-algebraic equations with properly stated leading term: A -critical points

Roswitha März and Ricardo Riaza

Mathematical and Computer Modelling of Dynamical Systems, 2007, vol. 13, issue 3, 291-314

Abstract: Time-domain models of dynamical systems are formulated in many applications in terms of differential-algebraic equations (DAEs). In the linear time-varying context, certain limitations of models of the form E ( t ) x ′( t ) + B ( t ) x ( t ) = q ( t ) have recently led to the properly stated formulation A ( t )( D ( t ) x ( t ))′ + B ( t ) x ( t ) =&# xA0; q ( t ), which allows for explicit descriptions of problem solutions in regular DAEs with arbitrary index, and provides precise functional input-output characterizations of the system. In this context, the present paper addresses critical points of linear DAEs with properly stated leading term; such critical points describe different types of singularities in the system. Critical points are classified according to a taxonomy which reflects the phenomenon from which the singularity stems; this taxonomy is proved independent of projectors and also invariant under linear time-varying coordinate changes and refactorizations. Under certain working assumptions, the analysis of such critical problems can be carried out through a scalarly implicit decoupling, yielding a singular inherent ODE. Certain harmless problems for which this decoupling can be rewritten in explicit form are characterized. Some electrical circuit applications, including a linear time-varying analogue of Chua's circuit, are discussed for illustrative purposes.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/13873950600883428 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:nmcmxx:v:13:y:2007:i:3:p:291-314

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/NMCM20

DOI: 10.1080/13873950600883428

Access Statistics for this article

Mathematical and Computer Modelling of Dynamical Systems is currently edited by I. Troch

More articles in Mathematical and Computer Modelling of Dynamical Systems from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().