Collinear dynamical systems

Jan Maximilian Montenbruck, Shen Zeng

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We introduce and study collinearity as a systems theoretic property, asking whether coupled dynamical systems with collinear initial conditions maintain collinear solutions for all times. Completely characterizing such collinear dynamical systems, we find that they define a Lie algebra whose Lie group are the invertible collinearity-preserving maps. Our characterization of collinear systems then allows us to determine state feedbacks which enforce collinear solutions in coupled control systems. Further, we characterize coupled linear differential equations whose solutions will asymptotically become collinear. Last, we characterize collinearity of multiple dynamical systems and their ability to produce coplanar solutions. Our findings relate to flows on the real projective spaces and Grassmannians.

Original languageEnglish
Pages (from-to)34-43
Number of pages10
JournalSystems and Control Letters
StatePublished - Jul 2017


  • Geometric approaches
  • Linear systems theory
  • Multi-agent systems


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