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Topological obstructions to stabilit...

Jongeneel, Wouter.

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Topological obstructions to stability and stabilization = history, recent advances and open problems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topological obstructions to stability and stabilization/ by Wouter Jongeneel, Emmanuel Moulay.
Reminder of title:	history, recent advances and open problems /
Author:	Jongeneel, Wouter.
other author:	Moulay, Emmanuel.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	x, 132 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Introduction -- 2. General topology -- 3. Diﬀerential topology -- 4. Algebraic topology -- 5. Dynamical control systems -- 6. Topological obstructions -- 7. Towards accepting and overcoming topological obstructions -- 8. Generalizations and open problems.
Contained By:	Springer Nature eBook
Subject:	Stability. -
Online resource:	https://doi.org/10.1007/978-3-031-30133-9
ISBN:	9783031301339

Topological obstructions to stability and stabilization = history, recent advances and open problems /
Jongeneel, Wouter.

Topological obstructions to stability and stabilizationhistory, recent advances and open problems /[electronic resource] :by Wouter Jongeneel, Emmanuel Moulay. - Cham :Springer Nature Switzerland :2023. - x, 132 p. :ill., digital ;24 cm. - SpringerBriefs in control, automation and robotics,2192-6794. - SpringerBriefs in control, automation and robotics..

1. Introduction -- 2. General topology -- 3. Diﬀerential topology -- 4. Algebraic topology -- 5. Dynamical control systems -- 6. Topological obstructions -- 7. Towards accepting and overcoming topological obstructions -- 8. Generalizations and open problems.

Open access.

This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk's retraction theory and the index-theoretic methodology of Krasnosel'skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.

ISBN: 9783031301339

Standard No.: 10.1007/978-3-031-30133-9doiSubjects--Topical Terms:

544228
Stability.

LC Class. No.: QA871

Dewey Class. No.: 514.3

Topological obstructions to stability and stabilization = history, recent advances and open problems /
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505 0 $a 1. Introduction -- 2. General topology -- 3. Diﬀerential topology -- 4. Algebraic topology -- 5. Dynamical control systems -- 6. Topological obstructions -- 7. Towards accepting and overcoming topological obstructions -- 8. Generalizations and open problems.
506 $a Open access.
520 $a This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk's retraction theory and the index-theoretic methodology of Krasnosel'skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
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