Attraction and Lyapunov stability for control systems on vector bundles

Attraction and Lyapunov stability for control systems on vector bundles

Let π:E→B be a finite-dimensional vector bundle whose base space is compact. In this paper, we study attraction and Lyapunov stability for control systems on E. We prove that, under certain conditions, the concepts of Conley attractor, uniform attractor, attractor, exponential attractor, asymptotica...

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Veröffentlicht in:Systems & control letters 2016-06, Vol.92, p.28-33
Hauptverfasser: Braga Barros, Carlos J., Rocha, Victor H.L.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Attraction
Bundles
Control systems
Equivalence
Lyapunov stability
Mathematical analysis
Stability
Vector bundles
Vectors (mathematics)
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Zusammenfassung:Let π:E→B be a finite-dimensional vector bundle whose base space is compact. In this paper, we study attraction and Lyapunov stability for control systems on E. We prove that, under certain conditions, the concepts of Conley attractor, uniform attractor, attractor, exponential attractor, asymptotically stable set and stable set are equivalent for the zero section of π:E→B.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2016.02.006