A time-stepping method for relay systems

W.P.M.H. Heemels, M.K. Camlibel, J.M. Schumacher

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

11 Citations (Scopus)
2 Downloads (Pure)


In this paper we will analyze a time-stepping method for the numerical simulation of dynamical systems containing Coulomb friction or relay characteristics. Time-stepping techniques replace the original dynamical system by a sequence of algebraic problems, that have to be solved for each time-step. For relay systems the one-step problem can be reformulated as a linear complementarity problem for which a wide range of solution algorithms already exists. As the event times at which the relay switches are "overstepped", the consistency of the method in the sense of the convergence of a sequence of approximations to an actual solution of the relay system can be put into question. However, in this paper we show that the proposed method is consistent even in the case that the event times accumulate (Zeno behavior). By an example we will illustrate how the method deals with Zeno trajectories
Original languageEnglish
Title of host publicationProceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
ISBN (Print)0-7803-6638-7
Publication statusPublished - 2000
Event39th IEEE Conference on Decision and Control (CDC 2000) - Sydney, Australia
Duration: 12 Dec 200015 Dec 2000


Conference39th IEEE Conference on Decision and Control (CDC 2000)
Abbreviated titleCDC 2000


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