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001 978-3-031-30133-9
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020 _a9783031301339
_9978-3-031-30133-9
024 7 _a10.1007/978-3-031-30133-9
_2doi
050 4 _aTJ212-225
072 7 _aTJFM
_2bicssc
072 7 _aGPFC
_2bicssc
072 7 _aTEC007000
_2bisacsh
072 7 _aTJFM
_2thema
082 0 4 _a629.8312
_223
082 0 4 _a003
_223
100 1 _aJongeneel, Wouter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTopological Obstructions to Stability and Stabilization
_h[electronic resource] :
_bHistory, Recent Advances and Open Problems /
_cby Wouter Jongeneel, Emmanuel Moulay.
250 _a1st ed. 2023.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2023.
300 _aX, 132 p. 27 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Control, Automation and Robotics,
_x2192-6794
505 0 _a1. 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. .
506 0 _aOpen Access
520 _aThis 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.
650 0 _aControl engineering.
650 0 _aDynamical systems.
650 0 _aTopology.
650 0 _aRobotics.
650 0 _aAlgorithms.
650 1 4 _aControl and Systems Theory.
650 2 4 _aDynamical Systems.
650 2 4 _aTopology.
650 2 4 _aRobotics.
650 2 4 _aDesign and Analysis of Algorithms.
700 1 _aMoulay, Emmanuel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031301322
776 0 8 _iPrinted edition:
_z9783031301346
830 0 _aSpringerBriefs in Control, Automation and Robotics,
_x2192-6794
856 4 0 _uhttps://doi.org/10.1007/978-3-031-30133-9
912 _aZDB-2-INR
912 _aZDB-2-SXIT
912 _aZDB-2-SOB
999 _c37657
_d37657