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024 7 $a10.1007/978-3-031-30133-9
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035   $a(DE-He213)978-3-031-30133-9
035   $a(PPN)270614591
035   $a(OCoLC)1379844604
035   $a(EXLCZ)995580000000542387
100   $a20230516d2023      u|             0
101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aTopological Obstructions to Stability and Stabilization$b[electronic resource] $eHistory, Recent Advances and Open Problems /$fby Wouter Jongeneel, Emmanuel Moulay
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023.
215   $a1 online resource (134 pages)
225 1 $aSpringerBriefs in Control, Automation and Robotics,$x2192-6794
311   $a3-031-30132-3 
327   $a1. Introduction -- 2. General topology -- 3. Di?erential topology -- 4. Algebraic topology -- 5. Dynamical control systems -- 6. Topological obstructions -- 7. Towards accepting and overcoming topological obstructions -- 8. Generalizations and open problems. .
330   $aThis open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk?s retraction theory and the index-theoretic methodology of Krasnosel?skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
410  0$aSpringerBriefs in Control, Automation and Robotics,$x2192-6794
606   $aControl engineering
606   $aDynamical systems
606   $aTopology
606   $aRobotics
606   $aAlgorithms
606   $aControl and Systems Theory
606   $aDynamical Systems
606   $aTopology
606   $aRobotics
606   $aDesign and Analysis of Algorithms
615  0$aControl engineering.
615  0$aDynamical systems.
615  0$aTopology.
615  0$aRobotics.
615  0$aAlgorithms.
615 14$aControl and Systems Theory.
615 24$aDynamical Systems.
615 24$aTopology.
615 24$aRobotics.
615 24$aDesign and Analysis of Algorithms.
676   $a629.8312
676   $a003
700   $aJongeneel$b Wouter$01363738
701   $aMoulay$b Emmanuel$01363739
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910725097803321
996   $aTopological Obstructions to Stability and Stabilization$93384782
997   $aUNINA