Journal of Dynamical and Control Systems

, Volume 13, Issue 3, pp 337–362 | Cite as

On Topological Equivalence of Linear Lows with Applications to Bilinear Control Systems

  • Victor Ayala
  • Fritz Colonius
  • Wolfgang Kliemann


This paper classifies continuous linear flows using concepts and techniques from topological dynamics. Specifically, the concepts of equivalence and conjugacy are adapted to flows on vector bundles, and the Lyapunov decomposition is characterized using the induced flows on the Grassmann and the flag bundles. These results are then applied to bilinear control systems, for which their behavior in \( \mathbb{R}^{d} \), on the projective space \(\mathbb{P}^{{d{\text{ - 1}}}} \), and on the Grassmannians is characterized.

Key words and phrases

Topological conjugacy linear flows bilinear control systems Grassmann graphs 

2000 Mathematics Subject Classification

37B55 37N35 93B10 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Victor Ayala
    • 1
  • Fritz Colonius
    • 2
  • Wolfgang Kliemann
    • 3
  1. 1.Departamento de MatematicasUniversidad Catolica del NorteAntofagastaChile
  2. 2.Institut für MathematikUniversität AugsburgAugsburgGermany
  3. 3.Department of MathematicsIowa State UniversityAmes IowaUSA

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