Topological Obstructions to Stability and Stabilization : History, Recent Advances and Open Problems (Springerbriefs in Electrical and Computer Engineering)

Jongeneel, Wouter/ Moulay, Emmanuel

Springer International Publishing AG（2023/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 132 p.
• 言語 ENG
• 商品コード 9783031301322
• DDC分類 629.8

Full Description

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 relatedfields.

Contents

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.