The chain control set of a linear control system
Adriano Da Silva
TL;DR
This paper investigates the properties of chain control sets in linear control systems on Lie groups, establishing that the compactness of a specific subgroup is key to their uniqueness and compactness.
Contribution
It provides a necessary and sufficient condition for the uniqueness and compactness of chain control sets in linear control systems on Lie groups.
Findings
Compactness of the central subgroup is necessary for chain control set uniqueness.
Compactness of the central subgroup is sufficient for chain control set compactness.
The main result links subgroup properties to control set characteristics.
Abstract
In this paper, we analyze the chain control sets of linear control systems on connected Lie groups. Our main result shows that the compactness of the central subgroup associated with the drift is a necessary and sufficient condition to assure the uniqueness and compactness of the chain control set.
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Taxonomy
TopicsPeroxisome Proliferator-Activated Receptors · Fibroblast Growth Factor Research · Functional Equations Stability Results