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Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation

Title data

Baier, Robert ; Braun, Philipp ; Grüne, Lars ; Kellett, Christopher M.:
Numerical Calculation of Nonsmooth Control Lyapunov Functions via Piecewise Affine Approximation.
In: IFAC-PapersOnLine. Vol. 52 (2019) Issue 16 . - pp. 370-375.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2019.11.808

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Official URL: Volltext

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Project information

Project title:
Project's official title
Project's id
Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov Functions
DP160102138

Project financing: ARC (Australian Research Council)

Abstract in another language

We review the numerical computation of control Lyapunov functions for switched systems in the Filippov sense and in the sample-and-hold sense. The computed (control) Lyapunov functions are piecewise affine and the decrease conditions involve either generalized gradients or the Dini subderivate. Further conditions for stabilization or stabilizability yield a (mixed) linear integer optimization problem.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: Contents:
1. Introduction
2. Problem
2.1 Setting
2.2 Stability notions
2.3 Lyapunov function charcterization
3. Piecewise Affine Approximation
4. Numerical Computation
5. Conclusion
Keywords: (control) Lyapunov function; asymptotic stability; controllability; switched systems; piecewise linear analysis; linear programming; mixed-integer problems
Subject classification: Mathematics Subject Classification Code: 93D30 (90C11 93D05 90C05)
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
Profile Fields > Advanced Fields > Nonlinear Dynamics
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 08 Jan 2020 12:24
Last Modified: 08 Feb 2021 08:36
URI: https://eref.uni-bayreuth.de/id/eprint/53682

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