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oapen-20.500.12657-635352023-06-21T04:20:59Z Topological Obstructions to Stability and Stabilization Jongeneel, Wouter Moulay, Emmanuel Control Systems Feedback Control Algebraic Topology Differential Topology Index Theory Retractive Theory Topological Obstruction bic Book Industry Communication::T Technology, engineering, agriculture::TJ Electronics & communications engineering::TJF Electronics engineering::TJFM Automatic control engineering bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBW Applied mathematics::PBWR Nonlinear science bic Book Industry Communication::T Technology, engineering, agriculture::TG Mechanical engineering & materials::TGM Materials science::TGMD Mechanics of solids::TGMD4 Dynamics & vibration bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBP Topology bic Book Industry Communication::U Computing & information technology::UY Computer science::UYQ Artificial intelligence bic Book Industry Communication::U Computing & information technology::UM Computer programming / software development::UMB Algorithms & data structures 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. 2023-06-20T10:21:15Z 2023-06-20T10:21:15Z 2023 book ONIX_20230620_9783031301339_3 9783031301339 9783031301322 https://library.oapen.org/handle/20.500.12657/63535 eng SpringerBriefs in Electrical and Computer Engineering; SpringerBriefs in Control, Automation and Robotics application/pdf n/a 978-3-031-30133-9.pdf https://link.springer.com/978-3-031-30133-9 Springer Nature Springer Nature Switzerland 10.1007/978-3-031-30133-9 10.1007/978-3-031-30133-9 6c6992af-b843-4f46-859c-f6e9998e40d5 07f61e34-5b96-49f0-9860-c87dd8228f26 9783031301339 9783031301322 Swiss National Science Foundation (SNF) Springer Nature Switzerland 132 Cham [...] Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung Swiss National Science Foundation open access
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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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