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  • © 2023

Topological Obstructions to Stability and Stabilization

History, Recent Advances and Open Problems

  • This book is open access, which means that you have free and unlimited access

  • Contains a detailed and accessible introduction to topology for the systems-and-control theorist

  • Includes the most popular and successful frameworks to overcome topological obstructions

  • Provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems

Part of the book series: SpringerBriefs in Electrical and Computer Engineering (BRIEFSELECTRIC)

Part of the book sub series: SpringerBriefs in Control, Automation and Robotics (BRIEFSCONTROL)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
  2. Introduction

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 1-19Open Access
  3. General Topology

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 21-27Open Access
  4. Differential Topology

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 29-47Open Access
  5. Algebraic Topology

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 49-55Open Access
  6. Dynamical Control Systems

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 57-75Open Access
  7. Topological Obstructions

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 77-107Open Access
  8. Towards Accepting and Overcoming Topological Obstructions

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 109-117Open Access
  9. Generalizations and Open Problems

    • Wouter Jongeneel, Emmanuel Moulay
    Pages 119-129Open Access
  10. Back Matter

    Pages 131-132

About this book

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.

Authors and Affiliations

  • Risk Analytics and Optimization Chair (RAO), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wouter Jongeneel

  • XLIM Research Institute (UMR CNRS 7252), University of Poitiers, Poitiers, France

    Emmanuel Moulay

About the authors

Wouter Jongeneel received the M.Sc. degree in Systems and Control from Delft University of Technology in 2019 and is currently pursuing the Ph.D. degree in Electrical Engineering at the École Polytechnique Fédérale de Lausanne (EPFL). His research is centered around the interplay of control, dynamical systems, optimization, and topology.  



Emmanuel Moulay received his M.S. degree in mathematics from the University of Lille, France, in 2002. He obtained his Ph.D. degree in automatic control in 2005 from the Ecole Centrale de Lille and his habilitation from the University of Poitiers in 2014. He joined the CNRS as a research scientist at the Ecole Centrale de Nantes in 2006 and moved at the XLIM institute of the University of Poitiers in 2009. He is also an adjunct professor in the department of Electrical and Computer Engineering at the University of Nebraska–Lincoln since 2020. His main interests are in control theory and its practical applications.


He has published over 100 research articles in international journals and conferences and worked on the topological obstructions to stability and stabilization; he has also published 2 book chapters in the Springer book series Lecture Notes in Control and Information Sciences.

Bibliographic Information

Buy it now

Buying options

Softcover Book USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access