On topological equivalence of linear lows with applications to bilinear control systems

Victor Ayala; Fritz Colonius; Wolfgang Kliemann

doi:10.1007/s10883-007-9021-9

On topological equivalence of linear lows with applications to bilinear control systems

Victor Ayala
, Fritz Colonius
, Wolfgang Kliemann

Universidad Católica del Norte
Augsburg University
Iowa State University

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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 ℝ ^d, on the projective space ℙ ^d-1, and on the Grassmannians is characterized.

Original language	English
Pages (from-to)	337-362
Number of pages	26
Journal	Journal of Dynamical and Control Systems
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/s10883-007-9021-9
State	Published - Jul 2007
Externally published	Yes

Keywords

Bilinear control systems
Grassmann graphs
Linear flows
Topological conjugacy

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10.1007/s10883-007-9021-9

Cite this

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abstract = "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 ℝ d, on the projective space ℙ d-1, and on the Grassmannians is characterized.",

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author = "Victor Ayala and Fritz Colonius and Wolfgang Kliemann",

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AU - Colonius, Fritz

AU - Kliemann, Wolfgang

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N2 - 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 ℝ d, on the projective space ℙ d-1, and on the Grassmannians is characterized.

AB - 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 ℝ d, on the projective space ℙ d-1, and on the Grassmannians is characterized.

KW - Bilinear control systems

KW - Grassmann graphs

KW - Linear flows

KW - Topological conjugacy

UR - https://www.scopus.com/pages/publications/34548665747

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DO - 10.1007/s10883-007-9021-9

M3 - Article

AN - SCOPUS:34548665747

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EP - 362

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 3

ER -

On topological equivalence of linear lows with applications to bilinear control systems

Abstract

Keywords

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