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Topological Obstructions to Stability and Stabilization
Wouter Jongeneel and Emmanuel Moulay
2023
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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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Keywords
- Algebraic topology
- Algorithms & data structures
- applied mathematics
- artificial intelligence
- Automatic control engineering
- Computer programming / software development
- Computer science
- Computing & information technology
- Control systems
- Differential topology
- Dynamics & vibration
- Electronics & communications engineering
- Electronics engineering
- feedback control
- Index Theory
- Materials science
- Mathematics
- Mathematics & science
- Mechanical engineering & materials
- Mechanics of solids
- Nonlinear science
- Retractive Theory
- Technology, engineering, agriculture
- Topological Obstruction
- Topology
Links
DOI: 10.1007/978-3-031-30133-9Editions