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(In-)Stability of Differential Inclusions

- Notions, Equivalences, and Lyapunov-like Characterizations
Af: Philipp Braun, Christopher M. Kellett, Lars Grune Engelsk Paperback

(In-)Stability of Differential Inclusions

- Notions, Equivalences, and Lyapunov-like Characterizations
Af: Philipp Braun, Christopher M. Kellett, Lars Grune Engelsk Paperback
Tjek vores konkurrenters priser

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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 116
ISBN-13: 9783030763169
Indbinding: Paperback
Udgave:
ISBN-10: 3030763161
Kategori: Regning og matematisk analyse
Udg. Dato: 13 jul 2021
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 13 jul 2021
Forfatter(e): Philipp Braun, Christopher M. Kellett, Lars Grune
Forfatter(e) Philipp Braun, Christopher M. Kellett, Lars Grune

Kategori Regning og matematisk analyse

ISBN-13 9783030763169

Sprog Engelsk

Indbinding Paperback

Sider 116

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 13 jul 2021

Oplagsdato 13 jul 2021

Forlag Springer Nature Switzerland AG

Kategori sammenhænge