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SpringerBriefs in Mathematics
cover

(In-)Stability of Differential Inclusions

Notions, Equivalences, and Lyapunov-like Characterizations

Authors: Braun, Philipp, Grüne, Lars, Kellett, Christopher M.

  • Offers a unified presentation of stability results for dynamical systems using Lyapunov-like characterizations
  • Provides derivation of strong/weak complete instability results for systems in terms of Lyapunov-like and comparison functions
  • Discusses combined stability and avoidance problem for control systems from the perspective of Lyapunov functions
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eBook 46,00 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: August 4, 2021
  • ISBN 978-3-030-76317-6
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover 57,19 €
price for Spain (gross)
  • Due: August 4, 2021
  • ISBN 978-3-030-76316-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.


About the authors

Philipp Braun received his Ph.D. in Applied Mathematics from the University of Bayreuth, Bayreuth, Germany, in 2016. He is a Research Fellow in the School of Engineering at the Australian National University, Canberra, Australia. His main research interests include control theory with a focus on stability analysis of nonlinear systems using Lyapunov methods and model predictive control.

Lars Grüne
received the Ph.D. in Mathematics from the University of Augsburg, Augsburg, Germany, in 1996 and the Habilitation from Goethe University Frankfurt, Frankfurt, Germany, in 2001. He is currently a Professor of Applied Mathematics with the University of Bayreuth, Bayreuth, Germany. His research interests include mathematical systems and control theory with a focus on numerical and optimization-based methods for nonlinear systems.

Christopher M. Kellett
received his Ph.D. in electrical and computer engineering from the University of California, Santa Barbara, in 2002. He is currently a Professor and the Director of the School of Engineering at Australian National University. His research interests are in the general area of systems and control theory with an emphasis on the stability, robustness, and performance of nonlinear systems with applications in both social and technological systems.

Buy this book

eBook 46,00 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: August 4, 2021
  • ISBN 978-3-030-76317-6
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover 57,19 €
price for Spain (gross)
  • Due: August 4, 2021
  • ISBN 978-3-030-76316-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
(In-)Stability of Differential Inclusions
Book Subtitle
Notions, Equivalences, and Lyapunov-like Characterizations
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-76317-6
DOI
10.1007/978-3-030-76317-6
Softcover ISBN
978-3-030-76316-9
Series ISSN
2191-8198
Edition Number
1
Number of Pages
VIII, 120
Number of Illustrations
1 b/w illustrations, 13 illustrations in colour
Topics