Title :
Area contraction of k-dimensional surfaces and almost global asymptotic stability
Author :
Aeyels, Dirk ; Smet, Filip De ; Langerock, Bavo
Author_Institution :
SYSTeMS research group, Department of Electrical Energy, Systems and Automation, Ghent University (UGent), Technologiepark-Zwijnaarde 914, 9052 Zwijnaarde, Belgium. E-mail: Dirk.Aeyels@UGent.be
Abstract :
In this paper we will formulate sufficient conditions for the area contraction of k-dimensional surfaces under the flow of a set of differential equations. We discuss the connection with the Hausdorff dimension of invariant sets and show how the presence of first integrals of the system influences these results. We conclude with an application to almost global asymptotic stability.
Keywords :
Hausdorff dimension; first integrals; k-contracting vector fields; Astronomy; Asymptotic stability; Automation; Density functional theory; Differential equations; Level set; Physics; Space technology; State-space methods; Sufficient conditions; Hausdorff dimension; first integrals; k-contracting vector fields;
Conference_Titel :
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on
Print_ISBN :
0-7803-9567-0
DOI :
10.1109/CDC.2005.1583454
