The nature of solutions to linear passive complementarity systems

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

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

6 Citations (Scopus)
79 Downloads (Pure)


Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the `complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of `regular states' turns out to be invariant under the dynamics
Original languageEnglish
Title of host publicationProceedings 38th IEEE Conference on Decision and Control, December 7-10, 1999, Phoenix AZ, USA
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
ISBN (Print)0-7803-5250-5
Publication statusPublished - 1999
Event38th IEEE Conference on Decision and Control (CDC 1999) - Phoenix, United States
Duration: 7 Dec 199910 Dec 1999
Conference number: 38


Conference38th IEEE Conference on Decision and Control (CDC 1999)
Abbreviated titleCDC 1999
CountryUnited States


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