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Complete Instability of Differential Inclusions using Lyapunov Methods

URN to cite this document: urn:nbn:de:bvb:703-epub-3630-6

Title data

Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Complete Instability of Differential Inclusions using Lyapunov Methods.
Bayreuth; Newcastle, Australia , 2018 . - 8 S.

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Project information

Project title:
Project's official titleProject's id
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov FunctionsDP160102138

Project financing: ARC (Australian Research Council)

Abstract

Abstract— Lyapunov functions and control Lyaupunov functions are a well established tool in the analysis of stability properties of dynamical systems as well as in the design of stabilizing feedback controllers. In order to address problems such as stabilization in the presence of unsafe sets of states or obstacle avoidance, one potential approach involves rendering such obstacles unstable by feedback. To this end we introduce (nonsmooth) Chetaev and control Chetaev functions and demonstrate their sufficiency for complete instability properties of dynamical systems. While a “time-reversal” approach is frequently used to study instability in reverse time of an asymptotically stable point in forward time, we demonstrate via an example that such an approach cannot be used to generate Chetaev functions from nonsmooth Lyapunov functions via a simple change of sign in the time argument.

Further data

Item Type: Preprint, postprint
Keywords: Lyapunov Methods; (Control) Chetaev Functions; (In)stability of Differential Inclusions; Complete Instability
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3630-6
Date Deposited: 19 Mar 2018 10:48
Last Modified: 28 Mar 2019 09:33
URI: https://epub.uni-bayreuth.de/id/eprint/3630

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