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Monotonicity on homogeneous spaces

Mostajeran, C and Sepulchre, R (2018) Monotonicity on homogeneous spaces. Mathematics of Control, Signals, and Systems, 30. ISSN 0932-4194

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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 with 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 induces orders that are tractable for use in analysis and propose invariant differential positivity as a natural generalization of monotonicity on such spaces.

Item Type: Article
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 21 Nov 2018 20:13
Last Modified: 15 Apr 2021 06:07
DOI: 10.1007/s00498-018-0229-x