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(In-)stability of differential inclu...

Braun, Philipp.

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	(In-)stability of differential inclusionsby Philipp Braun, Lars Grune, Christopher M. Kellett.
其他題名:	notions, equivalences, and Lyapunov-like characterizations /
作者:	Braun, Philipp.
其他作者:	Grune, Lars.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	ix, 116 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Lyapunov stability.
電子資源:	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 /
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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.
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