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024 7 $a10.1007/978-3-030-76317-6
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035   $a(OCoLC)1260293284
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035   $a(DE-He213)978-3-030-76317-6
035   $a(EXLCZ)995590000000534269
100   $a20210712d2021      u|         0
101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$a(In-)Stability of Differential Inclusions $eNotions, Equivalences, and Lyapunov-like Characterizations /$fby Philipp Braun, Lars Grüne, Christopher M. Kellett
205   $a1st ed. 2021.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021.
215   $a1 online resource (123 pages)
225 1 $aSpringerBriefs in Mathematics,$x2191-8201
311 08$a3-030-76316-1 
327   $a1 Introduction -- 2 Mathematical Setting & Motivation -- 3 Strong (in)stability of differential inclusions & Lyapunov characterizations -- 4 Weak (in)stability of differential inclusions & Lyapunov characterizations -- 5 Outlook & Further Topics -- 6 Proofs of the Main Results -- 7 Auxiliary results -- 8 Conclusions.
330   $aLyapunov methods have been and are still one of the main tools to analyze the stability properties of dynamical systems. In this monograph, Lyapunov results characterizing the stability and stability of the origin of differential inclusions are reviewed. To characterize instability and destabilizability, Lyapunov-like functions, called Chetaev and control Chetaev functions in the monograph, are introduced. Based on their definition and by mirroring existing results on stability, analogue results for instability are derived. Moreover, by looking at the dynamics of a differential inclusion in backward time, similarities and differences between stability of the origin in forward time and instability in backward time, and vice versa, are discussed. Similarly, the invariance of the stability and instability properties of the equilibria of differential equations with respect to scaling are summarized. As a final result, ideas combining control Lyapunov and control Chetaev functions to simultaneously guarantee stability, i.e., convergence, and instability, i.e., avoidance, are outlined. The work is addressed at researchers working in control as well as graduate students in control engineering and applied mathematics.
410  0$aSpringerBriefs in Mathematics,$x2191-8201
606   $aMathematics
606   $aMathematics
615  0$aMathematics.
615 14$aMathematics.
676   $a003.71
700   $aBraun$b Philipp$01069703
702   $aKellett$b Christopher M.
702   $aGru?ne$b Lars$f1967-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910492152103321
996   $aIn-)stability of differential inclusions$92819213
997   $aUNINA