Monotonicity on homogeneous spaces
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Mostajeran, C
Sepulchre, Rodolphe https://orcid.org/0000-0002-7047-3124
Abstract
This paper presents a formulation of the notion of monotonicity on homogeneous spaces. We review the general theory of invariant cone fields on homogeneous spaces and provide a list of examples involving spaces that arise in applications in information engineering and applied mathematics. Invariant cone fields associate a cone to the tangent space at each point in a way that is invariant with respect to the group actions that define the homogeneous space. We argue that invariance of conal structures induce orders that are tractable for use in analysis and propose invariant differential positivity as a natural generalization of monotonicity on such spaces.
Description
Keywords
Monotone systems, Homogeneous spaces, Positivity, Cone fields, 34C12, 37C65, 22F30, 06A75
Journal Title
Mathematics of Control, Signals, and Systems
Conference Name
Journal ISSN
0932-4194
1435-568X
1435-568X
Volume Title
30
Publisher
Springer Science and Business Media LLC
Publisher DOI
Sponsorship
EPSRC (1355845)
European Research Council (670645)
European Research Council (670645)
ERC