國立高雄大學圖資館 |

Language: English

Back

(In-)stability of differential inclu...

Braun, Philipp.

(In-)stability of differential inclusionsnotions, equivalences, and Lyapunov-like characterizations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	(In-)stability of differential inclusionsby Philipp Braun, Lars Grune, Christopher M. Kellett.
Reminder of title:	notions, equivalences, and Lyapunov-like characterizations /
Author:	Braun, Philipp.
other author:	Grune, Lars.
Published:	Cham :Springer International Publishing :2021.
Description:	ix, 116 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Lyapunov stability.
Online resource:	https://doi.org/10.1007/978-3-030-76317-6
ISBN:	9783030763176$q(electronic bk.)

(In-)stability of differential inclusionsnotions, equivalences, and Lyapunov-like characterizations /
Braun, Philipp.

(In-)stability of differential inclusionsnotions, equivalences, and Lyapunov-like characterizations /[electronic resource] :by Philipp Braun, Lars Grune, Christopher M. Kellett. - Cham :Springer International Publishing :2021. - ix, 116 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

1 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.

Lyapunov 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.

ISBN: 9783030763176$q(electronic bk.)

Standard No.: 10.1007/978-3-030-76317-6doiSubjects--Topical Terms:

338007
Lyapunov stability.

LC Class. No.: QA871 / .B73 2021

Dewey Class. No.: 515.39

(In-)stability of differential inclusionsnotions, equivalences, and Lyapunov-like characterizations /
LDR:02665nmm a2200337 a 4500 001 602532
003 DE-He213
005 20210712133928.0
006 m d
007 cr nn 008maaau
008 211112s2021 sz s 0 eng d
020 $a 9783030763176$q(electronic bk.)
020 $a 9783030763169$q(paper)
024 7 $a 10.1007/978-3-030-76317-6 $2 doi
035 $a 978-3-030-76317-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA871 $b .B73 2021
072 7 $a PB $2 bicssc
072 7 $a MAT000000 $2 bisacsh
072 7 $a PB $2 thema
082 0 4 $a 515.39 $2 23
090 $a QA871 $b .B825 2021
100 1 $a Braun, Philipp. $3 898247
245 1 0 $a (In-)stability of differential inclusions $h [electronic resource] : $b notions, equivalences, and Lyapunov-like characterizations / $c by Philipp Braun, Lars Grune, Christopher M. Kellett.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a ix, 116 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a 1 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.
520 $a Lyapunov 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.
650 0 $a Lyapunov stability. $3 338007
650 0 $a Differential equations. $3 183925
650 1 4 $a Mathematics, general. $3 274849
700 1 $a Grune, Lars. $3 469280
700 1 $a Kellett, Christopher M. $3 898248
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u https://doi.org/10.1007/978-3-030-76317-6
950 $a Mathematics and Statistics (SpringerNature-11649)