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

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Open access

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

9783031301339 (electronic bk.)
3031301331 (electronic bk.)
9783031301322
3031301323

Cham : Springer, [2023]

©2023

English

1 online resource (x, 132 pages) : illustrations.

10.1007/978-3-031-30133-9 doi

QA871

514/.3

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.

Includes bibliographical references.

Open access

Online resource; title from PDF title page (SpringerLink, viewed May 24, 2023).

SpringerBriefs in electrical and computer engineering. Control, automation and robotics.

Print version: 9783031301322

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