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Differential positivity with respect to cones of rank k ≥ 2

Accepted version
Peer-reviewed

Type

Conference Object

Change log

Authors

Mostajeran, CS 
Sepulchre, Rodolphe  ORCID logo  https://orcid.org/0000-0002-7047-3124

Abstract

We consider a generalized notion of differential positivity of a dynamical system with respect to cone fields generated by cones of rank k. The property refers to the contraction of such cone fields by the linearization of the flow along trajectories. It provides the basis for a generalization of differential Perron-Frobenius theory, whereby the Perron-Frobenius vector field which shapes the one-dimensional attractors of a differentially positive system is replaced by a distribution of rank k that results in k-dimensional integral submanifold attractors instead. We further develop the theory in the context of invariant cone fields and invariant differential positivity on Lie groups and illustrate the key ideas with an extended example involving consensus on the space of rotation matrices SO(3).

Description

Keywords

Positivity, Differential Analysis, Monotone Systems, Manifolds, Lie Groups, Consensus, Synchronization

Journal Title

20th IFAC World Congress

Conference Name

20th International Federation of Automatic Control World Congress

Journal ISSN

2405-8963

Volume Title

50

Publisher

Elsevier
Sponsorship
EPSRC (1355845)
The Royal Society (wm130007)
European Research Council (670645)
C. Mostajeran is supported by the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom. The research leading to these results has also received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n.670645