Stability and controllability of planar bimodal linear complementarity systems

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

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

39 Citations (Scopus)


The object of study of this paper is the class of hybrid systems consisting of so-called linear complementarity (LC) systems, that received a lot of attention recently and has strong connections to piecewise affine (PWA) systems. In addition to PWA systems, some of the linear or affine submodels of the LC systems can 'live' at lower-dimensional subspaces and re-initializations of the state variable at mode changes is possible. For LC systems we study the stability and controllability problem. Although these problems received for various classes of hybrid systems ample attention, necessary and sufficient conditions, which are explicit and easily verifiable, are hardly found in the literature. For LC systems with two modes and a state dimension of two such conditions are presented.

Original languageEnglish
Title of host publication42nd IEEE International Conference on Decision and Control
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Print)0-7803-7924-1
Publication statusPublished - 1 Dec 2003
Event42nd IEEE Conference on Decision and Control (CDC 2003) - Hyatt Regency Maui, Maui, United States
Duration: 9 Dec 200312 Dec 2003
Conference number: 42


Conference42nd IEEE Conference on Decision and Control (CDC 2003)
Abbreviated titleCDC 2003
Country/TerritoryUnited States


  • Complementarity systems
  • Controllability
  • Hybrid systems
  • Planar systems
  • Stability


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